MATRICES-(E)-06-ASSIGNMENT

1. If be a diagonal matrix, then (a) 2 (b) 0 (c) 1 (d) 3 2. Which of the following is a diagonal matrix (a) (b) (c) (d) None of these 3. If I is a unit matrix, then will be (a) A unit matrix (b) A triangular matrix (c) A scalar matrix (d) None of these 4. If , then the value of X where A+X is a unit matrix, is (a) (b) (c) (d) None of these 5. If A is diagonal matrix of order , then wrong statement is (a) , where B is a diagonal matrix of order (b) AB is a diagonal matrix (c) (d) A is a scalar matrix 6. If and , then (a) –2 (b) 2 (c) –4 (d) 4 7. If and , then the correct relation is (a) (b) (c) (d) None of these 8. If and , then (a) (b) (c) (d) 9. If , then (a) (b) (c) (d) 10. If , then (a) A (b) 2A (c) – A (d) –2A 11. If , then (a) (b) (c) (d) None of these 12. If and , then (a) (2, 3) (b) (3, 4) (c) (4, 3) (d) None of these 13. If , and and differs by , then AB = (a) I (b) O (c) –I (d) None of these 14. If and , then AB = (a) (b) (c) (d) 15. If and , then (a) (b) (c) (d) None of these 16. If ,then for what value of (a) 0 (b) (c) –1 (d) 1 17. If and , then the minimum value of n is (a) 2 (b) 3 (c) 4 (d) 5 18. If , and AB = I, then x = (a) –1 (b) 1 (c) 0 (d) 2 19. If and , then (a) (b) (c) (d) None of these 20. If A=[1 2 3] and , then (a) (b) (c) (d) 21. If and , then is (a) Diagonal matrix (b) Null matrix (c) Unit matrix (d) None of these 22. If , then (a) (b) (c) (d) 23. If and , then (a) (b) (c) (d) 24. If ,then (a) (b) (c) (d) None of these 25. If and ,then (a) (b) (c) (d) None of these 26. If ,then is equal to (a) (b) (c) (d) 27. If , then (a) (b) (c) (d) 28. If and , then (a) (b) (c) (d) 29. If and , where I and O are unit and null matrices of order 3 respectively, then (a) (b) (c) (d) 30. If and I is the identity matrix of order 2, then (a) I (b) O (c) (d) 31. If , then (a) (b) (c) (d) 32. If , then (a) (b) (c) (d) 33. If , then the value of is (a) (b) (c) (d) None of these 34. If , then (a) (b) (c) (d) 35. If and , then (a) (b) (c) (d) None of these 36. If , B , then (a) (b) (c) (d) 37. If , , then (a) (b) (c) (d) None of these 38. If , then (a) (b) (c) (d) 39. If , , then (a) (b) (c) (d) 40. If , I is the unit matrix of order 2 and a, b are arbitrary constants, then is equal to (a) (b) (c) (d) None of these 41. If , , and , then (a) 20 (b) [–20] (c) –20 (d) [20] 42. Which one of the following is not true (a) Matrix addition is commutative (b) Matrix addition is associative (c) Matrix multiplication is commutative (d) Matrix multiplication is associative 43. If , and , then which of the following is defined (a) AB (b) BA (c) (d) 44. If and I is a unit matrix of 3rd order, then equals (a) 2A (b) 4A (c) 6A (d) None of these 45. If , then equals (a) (b) (c) (d) 46. (a) [–1] (b) (c) (d) Not defined 47. If , then X is equal to (a) (b) (c) (d) None of these 48. If and , then the values of are respectively (a) –6, –12, –18 (b) –6, 4, 9 (c) –6, –4, –9 (d) –6, 12, 18 49. If , then (a) (b) (c) (d) 50. If matrix , then (a) (b) (c) (d) 51. If , then (a) I (b) 14I (c) 0 (d) None of these 52. If , then (a) (b) (c) (d) None of these 53. Which is true about matrix multiplication (a) It is commutative (b) It is associative (c) Both (a) and (b) (d) None of these 54. If and , then PQ is equal to (a) (b) (c) (d) 55. is equal to (a) (b) (c) (d) 56. If , , then AB is (a) (b) (c) (d) 57. For matrices A, B and I, if and , then A equals [AMU 1992] (a) (b) (c) (d) 58. If , then equals (a) A (b) 2 A (c) 3 A (d) 4 A 59. If and , then AB equals (a) (b) (c) (d) 60. Let , , then (a) (b) (c) (d) 61. If A, B are square matrices of order , then is equal to (a) (b) (c) (d) 62. If and , then is equal to (a) (b) (c) (d) None of these 63. If , , then is equal to (a) (b) (c) (d) 64. If , and , then equals (a) (b) (c) (d) 65. If , and , then equals (a) (b) (c) (d) 66. If , then x and y are (a) 1, 1 (b) 1, 2 (c) 2, 2 (d) 2, 1 67. If and , then the value of a is (a) –2 (b) 0 (c) 2 (d) 1 68. If and , then (a) (b) (c) (d) None of these 69. If and , then AB is equal to (a) (b) (c) (d) None of these 70. If and , then AB equals (a) (b) (c) (d) 71. , then A equals (a) (b) (c) (d) 72. If , and , then which of the following is not defined [MP PET 1987] (a) AB (b) (c) (d) 73. If a matrix B is obtained by multiplying each element of a matrix A of order by 3, then relation between A and B is (a) (b) (c) (d) 74. For each real number x such that , let be the matrix and . Then (a) (b) (c) (d) 75. If , then the value of is (a) (b) (c) (d) 76. If , then (a) (b) (c) (d) 77. If and I is the unit matrix of order 2, then equals (a) (b) (c) (d) 78. If , then (a) (b) (c) (d) None of these 79. If , then which of following statement is true (a) and (b) and (c) and (d) and 80. , if and only if (a) (b) (c) (d) None of these 81. If , then the order of A is (a) (b) (c) (d) 82. If , then matrices A, B, C are (a) (b) (c) (d) 83. is a square matrix, if (a) (b) (c) (d) None of these 84. If and , then the element of 3rd row and third column in AB will be (a) –18 (b) 4 (c) –12 (d) None of these 85. If A and B be symmetric matrices of the same order, then will be a (a) Symmetric matrix (b) Skew-symmetric matrix (c) Null matrix (d) None of these 86. If A and B are square matrices of order 2, then (a) (b) (c) (d) None of these 87. If the order of the matrices A and B be and respectively, then the order of will be (a) (b) (c) (d) None of these 88. In a lower triangular matrix element , if (a) (b) (c) (d) 89. If A is a square matrix of order n and , where is a scalar, then (a) (b) (c) (d) 90. Let , and . The expression which is not defined is (a) (b) (c) (d) 91. If , and , then the correct statement is (a) (b) (c) (d) 92. If A and B are two matrices and , then (a) (b) (c) (d) None of these 93. If A and B are square matrices of same order, then (a) (b) (c) (d) 94. Which of the following is incorrect (a) (b) (c) , where A,B commute (d) 95. Which of the following is/are incorrect (i) Adjoint of a symmetric matrix is symmetric, (ii) Adjoint of unit matrix is a unit matrix, (iii) and (iv) Adjoint of a diagonal matrix is a diagonal matrix (a) (i) (b) (ii) (c) (iii) and (iv) (d) None of these 96. Let be a square matrix and let be cofactor of in A. If , then (a) (b) (c) (d) None of these 97. A, B are n-rowed square matrices such that and B is non-singular. Then (a) (b) (c) (d) None of these 98. If A and B are two matrices such that and , then (a) 2 AB (b) 2 BA (c) (d) AB 99. If A and B are two matrices such that and AB are both defined, then (a) A and B are two matrices not necessarily of same order (b) A and B are square matrices of same order (c) Number of columns of A= number of rows of B (d) None of these 100. If and is the identity matrix, then x = (a) 1 (b) 2 (c) 3 (d) 0 101. If , , then equals (a) (b) (c) (d) None of these 102. If and , then is equal to (a) (b) (c) (d) None of these 103. If A is matrix and B is a matrix such that and are both defined. Then B is of the type (a) (b) (c) (d) 104. Which of the following is not true (a) Every skew-symmetric matrix of odd order is non-singular (b) If determinant of a square matrix is non-zero, then it is non-singular (c) Adjoint of a symmetric matrix is symmetric (d) Adjoint of a diagonal matrix is diagonal 105. Which one of the following statements is true (a) Non-singular square matrix does not have a unique inverse (b) Determinant of a non-singular matrix is zero (c) If , then A is a square matrix (d) If , then where 106. If matrix , then (a) (b) (c) (d) , where is a non-zero scalar 107. If and , then (a) (b) (c) (d) 108. Which one of the following is correct (a) Skew-symmetric matrix of odd order is non-singular. (b) Skew-symmetric matrix of odd order is singular (c) Skew-symmetric matrix of even order is always singular (d) None of these 109. Choose the correct answer (a) Every identity matrix is a scalar matrix (b) Every scalar matrix is an identity matrix (c) Every diagonal matrix is an identity matrix (d) A square matrix whose each element is 1 is an identity matrix. 110. If A and B are two square matrices such that , then = (a) 0 (b) (c) (d) 111. For a matrix A, and is true for (a) If A is a square matrix (b) If A is a non singular matrix (c) If A is a symmetric matrix (d) If A is any matrix 112. If two matrices A and B are of order and respectively, can be subtracted only, if (a) (b) (c) (d) None of these 113. The set of all matrices over the real numbers is not a group under matrix multiplication because (a) Identity element does not exist (b) Closure property is not satisfied (c) Association property is not satisfied (d) Inverse axiom may not be satisfied 114. If the matrix , then (a) or (b) and (c) It is not necessary that either or (d) 115. If and , then A is equal to (a) (b) (c) (d) None of these 116. Assuming that the sums and products given below are defined, which of the following is not true for matrices (a) (b) does not imply (c) implies or (d) 117. Which of the following is true for matrix AB (a) (b) (c) (d) All of these 118. If A and B are matrices such that and , then (a) and (b) and (c) and (d) and 119. If A and B are symmetric matrices of order , then (a) is skew symmetric (b) is symmetric (c) is a diagonal matrix (d) is a zero matrix 120. The possible number of different order which a matrix can have when it has 24 elements is (a) 6 (b) 8 (c) 4 (d) 10 121. If and , then minimum value of n is (a) 2 (b) 4 (c) 5 (d) 3 122. If A, B, C are square matrices of the same order, then which of the following is true (a) (b) (c) or (d) 123. If a matrix has 13 elements, then the possible dimensions (order) it can have are (a) (b) (c) (d) None of these 124. If A, B, C are three matrices, then (a) (b) (c) (d) 125. If , then = (a) 14 (b) (c) (d) None of these 126. If , then equals (a) (b) (c) (d) None of these 127. If and , then (a) (b) (c) (d) 128. If and , then is equal to (a) (b) (c) (d) None of these 129. If , then (a) (b) (c) (d) None of these 130. Transpose of a row matrix is a (a) Row matrix (b) Column matrix (c) A square matrix (d) A scalar matrix 131. If and , then correct statement is (a) (b) (c) (d) None of these 132. If matrix A is of order and B is of order , then order of is equal to (a) Order of AB (b) Order of BA (c) Order of (d) Order of 133. If , then is (a) (b) (c) (d) 134. Let A is a skew-symmetric matrix and C is a column matrix, then is (a) (b) (c) (d) 135. If A and B are matrices of suitable order and k is any number, then correct statement is (a) (b) (c) (d) 136. If A and B are matrices of suitable order, then wrong statement is (a) (b) (c) (d) 137. If A is a square matrix such that , then , where A’ is transpose of A, is equal to (a) 0 (b) –2 (c) 1/2 (d) 2 138. An orthogonal matrix is (a) (b) (c) (d) 139. Matrix is (a) Orthogonal (b) Idempotent (c) Skew-symmetric (d) Symmetric 140. The inverse of a symmetric matrix is (a) Symmetric (b) Skew-symmetric (c) Diagonal matrix (d) None of these 141. If A is a symmetric matrix and , then is (a) Symmetric (b) Skew-symmetric (c) A diagonal matrix (d) None of these 142. If A is a skew-symmetric matrix and n is a positive integer, then is (a) A symmetric matrix (b) Skew-symmetric matrix (c) Diagonal matrix (d) None of these 143. If is symmetric, then (a) 3 (b) 5 (c) 2 (d) 4 144. If A is a square matrix, then is (a) Non-singular matrix (b) Symmetric matrix (c) Skew-symmetric matrix (d) Unit matrix 145. For any square matrix A, is a (a) Unit matrix (b) Symmetric matrix (c) Skew-symmetric matrix (d) Diagonal matrix 146. If A is a square matrix for which , then A is (a) Zero matrix (b) Unit matrix (c) Symmetric matrix (d) Skew-symmetric matrix 147. If A is a square matrix and is symmetric matrix, then (a) Unit matrix (b) Symmetric matrix (c) Skew-symmetric matrix (d) Zero matrix 148. The value of a for which the matrix is singular if (a) (b) (c) (d) 149. The matrix is which of the following (a) Symmetric (b) Skew-symmetric (c) Hermitian (d) Skew-hermitian 150. The matrix, is nilpotent of index (a) 2 (b) 3 (c) 4 (d) 6 151. If is symmetric matrix, then (a) (b) (c) (d) 152. The matrix is a (a) Non-singular (b) Idempotent (c) Nilpotent (d) Orthogonal 153. For any square matrix A, which statement is wrong (a) (b) (c) (d) None of these 154. If , then A is (a) An upper triangular matrix (b) A null matrix (c) A lower triangular matrix (d) None of these 155. If A is a square matrix, then A will be non-singular if (a) (b) (c) (d) 156. The matrix is (a) Symmetric (b) Skew-symmetric (c) Scalar (d) None of these 157. If , then is (a) Null matrix (b) Unit matrix (c) A (d) 2A 158. If A is a symmetric matrix, then matrix is (a) Symmetric (b) Skew-symmetric (c) Hermitian (d) Skew-Hermitian 159. If A is a square matrix, then which of the following matrices is not symmetric (a) (b) (c) (d) 160. Square matrix will be an upper triangular matrix, if (a) for (b) for (c) for (d) None of these 161. If the matrix is singular, then (a) –2 (b) –1 (c) 1 (d) 2 162. In order that the matrix be non-singular, should not be equal to (a) 1 (b) 2 (c) 3 (d) 4 163. If A is involutory matrix and and I is unit matrix of same order, then is (a) Zero matrix (b) A (c) I (d) 2A 164. If , then A is (a) Symmetric (b) Skew-symmetric (c) Non-singular (d) Singular 165. If , then (a) Unit matrix (b) Null matrix (c) A (d) – A 166. If the matrix is singular, then (a) –2 (b) 4 (c) 2 (d) –4 167. Out of the following a skew-symmetric matrix is (a) 3 (b) 3 (c) 3 (d) 3 If 3 , then A is (a) Singular (b) Non-singular (c) Unitary (d) Symmetric 168. If A, B, C are three square matrices such that implies , then the matrix A is always (a) A singular matrix (b) A Non-singular matrix (c) An orthogonal matrix (d) A diagonal matrix 169. The matrix is (a) Unitary (b) Orthogonal (c) Nilpotent (d) Involutary 170. If a matrix A is symmetric as well as skew symmetric, then (a) A is a diagonal matrix (b) A is a null matrix (c) A is a unit matrix (d) A is a triangular matrix. 171. A and B are any two square matrices. Which one of the following is a skew symmetric matrix (a) (b) (c) (d) None of the above. 172. Choose the correct answer (a) Every scalar matrix is an identity matrix (b) Every identity matrix is a scalar matrix (c) Every diagonal matrix is an identity matrix (d) A Square matrix whose each element is 1 is an identity matrix 173. For a square matrix A, it is given that , then A is a (a) Orthogonal matrix (b) Diagonal matrix (c) Symmetric matrix (d) None of these 174. A square matrix can always be expressed as a (a) Sum of a symmetric matrix and a skew-symmetric matrix (b) Sum of a diagonal matrix and a symmetric matrix (c) Skew matrix (d) Skew- symmetric matrix 175. If A is a skew-symmetric matrix and n is odd positive integer, then is (a) A symmetric matrix (b) A skew-symmetric matrix (c) A diagonal matrix (d) None of these 176. If A, B symmetric matrices of the same order then AB – BA is (a) Symmetric matrix (b) Skew-symmetric matrix (c) Null matrix (d) Unit matrix 177. If k is a scalar and I is a unit matrix of order 3, then (a) (b) (c) (d) 178. If , then (a) A (b) I (c) O (d) 179. If A is a matrix, then (a) (b) (c) (d) None of these 180. Adjoint of the matrix is (a) N (b) 2N (c) – N (d) None of these 181. If A is a non-singular matrix, then (a) A (b) I (c) (d) 182. If and , then k is equal to (a) 0 (b) 1 (c) (d) 183. Let , then the adjoint of A is (a) (b) (c) (d) None of these 184. If , then (a) (b) (c) (d) None of these 185. If A is a singular matrix, then is (a) Singular (b) Non-singular (c) Symmetric (d) Not defined 186. The adjoint of is (a) (b) (c) (d) None of these 187. (a) (b) I (c) O (d) None of these 188. If , then (a) (b) (c) (d) None of these 189. If , then the value of is (a) 36 (b) 72 (c) 144 (d) None of these 190. If A is a matrix of order 3 and = 8, then (a) 1 (b) 2 (c) (d) 191. If A and B are non-singular square matrices of same order, then is equal to (a) (b) (c) (d) 192. If d is the determinant of a square matrix A of order n, then the determinant of its adjoint is (a) (b) (c) (d) d 193. If , then is equal to (a) (b) (c) (d) 194. If , then (a) I (b) (c) (d) None of these 195. If , then is (a) (b) (c) (d) None of these 196. The adjoint matrix of is (a) (b) (c) (d) 197. If , then (a) (b) (c) (d) 198. If , then the value of is (a) (b) (c) (d) 199. If , then the value of is (a) (b) (c) (d) 200. If , then determinant is (a) (b) (c) (d) 201. If A is a square matrix, then is equal to (a) (b) (c) Null matrix (d) Unit matrix 202. If , then is equal to (a) 13 (b) – 13 (c) 5 (d) – 5 203. For a third order non-singular matrix A, equals (a) (b) (c) (d) None of these 204. If A be a square matrix of order n and if and , then (a) (b) (c) (d) None of these 205. Inverse of the matrix is (a) (b) (c) (d) 206. If A and B are non-singular matrices, then (a) (b) (c) (d) 207. If , then (a) (b) (c) (d) 208. If , then (a) (b) (c) (d) None of these 209. If , then (a) (b) (c) (d) None of these 210. The element of second row and third column in the inverse of is (a) – 2 (b) – 1 (c) 1 (d) 2 211. The inverse of the matrix is (a) (b) (c) (d) 212. The inverse of is (a) (b) (c) (d) 213. The inverse of the matrix is (a) (b) (c) (d) 214. If a matrix A is such that , then its inverse is (a) (b) (c) (d) None of these 215. If and , then (a) (b) (c) (d) 216. If and , then (a) (b) (c) (d) None of these 217. If , then the matrix (a) (b) (c) (d) 218. If A is an invertible matrix, then which of the following is correct (a) is multivalued (b) is singular (c) (d) 219. If , then = (a) (b) (c) (d) None of these 220. (a) (b) (c) (d) 221. If , then (a) (b) (c) (d) 222. (a) (b) (c) (d) 223. The inverse of matrix is (a) A (b) (c) (d) 224. The inverse of is (a) (b) (c) (d) None of these 225. The inverse of is (a) (b) (c) (d) None of these 226. The matrix is invertible, if (a) (b) (c) (d) 227. If , then is equal to (a) (b) (c) (d) 228. The matrix is not invertible, if ‘a’ has the value (a) 2 (b) 1 (c) 0 (d) – 1 229. Inverse matrix of (a) (b) (c) (d) 230. If the multiplicative group of matrices of the form , for and , then the inverse of is (a) (b) (c) (d) Does not exist 231. The element in the first row and third column of the inverse of the matrix is (a) – 2 (b) 0 (c) 1 (d) 7 232. If is the identity matrix of order 3, then is (a) 0 (b) (c) (d) Does not exist 233. If a matrix A is such that , then equals (a) (b) (c) (d) 234. If and , then (a) (b) (c) (d) 235. If , then (a) (b) (c) (d) 236. If , then (a) (b) (c) (d) Does not exist 237. If for the matrix A, , then (a) (b) (c) A (d) None of these 238. For two invertible matrices A and B of suitable orders, the value of is (a) (b) (c) (d) 239. If and , , then (a) (b) (c) (d) 240. If , then (a) (b) (c) (d) 241. If and , then (a) (b) (c) (d) 242. The multiplicative inverse of matrix is (a) (b) (c) (d) 243. The inverse matrix of is (a) (b) (c) (d) 244. Inverse of the matrix is (a) (b) (c) (d) 245. If A is an orthogonal matrix, then is equal to (a) A (b) (c) (d) None of these 246. The multiplicative inverse of the matrix is (a) (b) (c) (d) 247. Let A be an invertible matrix. Which of the following is not true (a) (b) (c) (d) None of these 248. Inverse of is (a) (b) (c) (d) None of these 249. If , then (a) (b) (c) (d) 250. If , and , then is equal to (a) (b) (c) (d) 251. If for a square matrix A, , then A is (a) Orthogonal matrix (b) Symmetric matrix (c) Diagonal matrix (d) Invertible matrix 252. If matrix is invertible, then (a) (b) (c) (d) 253. If , then (a) (b) (c) (d) None of these 254. If , then (a) (b) (c) (d) 255. If is a cube root of unity and , then (a) (b) (c) (d) 256. If , then (a) A (b) (c) (d) 257. If , where for all , then is equal to (a) D (b) (c) I (d) None of these 258. If , then is equal to (a) diag (b) diag (c) A (d) None of these 259. If A is a square matrix of order 3, then true statement is (where I is unit matrix) (a) det (b) det A = 0 (c) det (d) det 2A = 2 det A 260. If and , then is equal to (a) 4 (b) 8 (c) 16 (d) 32 261. If A and B are square matrices of order 3 such that , then (a) – 9 (b) – 81 (c) – 27 (d) 81 262. Which of the following is correct (a) Determinant is a square matrix (b) Determinant is a number associated to a matrix (c) Determinant is a number associated to a square matrix (d) None of these 263. Let A be a skew-symmetric matrix of odd order, then is equal to (a) 0 (b) 1 (c) –1 (d) None of these 264. Let A be a skew-symmetric matrix of even order, then (a) Is a perfect square (b) Is not a perfect square (c) Is always zero (d) None of these 265. For any matrix A, if A(adj.A) , then (a) 0 (b) 10 (c) 20 (d) 100 266. If , then determinant of is (a) 5 (b) 25 (c) – 5 (d) – 25 267. If is a singular matrix, then x is (a) (b) (c) (d) 268. The product of a matrix and its transpose is an identity matrix. The value of determinant of this matrix is (a) – 1 (b) 0 (c) (d) 1 269. If , then det A = [EAMCET 2002] (a) 2 (b) 3 (c) 4 (d) 5 270. If and are matrix such that , then (a) or (b) and (c) (d) 271. If A is a square matrix such that , then det (A) equals (a) 0 or 1 (b) – 2 or 2 (c) – 3 or 3 (d) None of these 272. If A is a square matrix such that , then for any +ve integer n, is equal to (a) 0 (b) 2n (c) (d) 273. If A is a square matrix of order 3 and entries of A are positive integers, then is (a) Different from zero (b) 0 (c) Positive (d) An arbitrary integer. 274. If A and B are any matrix, then det implies (a) (b) or (c) and (d) None of these 275. If , then (x, y, z) = (a) (4, 3, 2) (b) (3, 2, 4) (c) (2, 3, 4) (d) None of these 276. The solution of the equation is (x, y, z) = (a) (1, 1, 1) (b) (0, –1, 2) (c) (–1, 2, 2) (d) (–1, 0, 2) 277. If , and , then X is equal to (a) (b) (c) (d) 278. If A is a non-zero column matrix of order and B is a non-zero row matrix of order , then rank of AB is equal to (a) m (b) n (c) 1 (d) None of these 279. If , then (a) (b) (c) (d) None of these 280. If is the identity matrix of order n, then rank of is (a) 1 (b) n (c) 0 (d) None of these 281. The rank of a null matrix is (a) 0 (b) 1 (c) Does not exist (d) None of these 282. If A is a non-singular square matrix of order n, then the rank of A is (a) Equal to n (b) Less then n (c) Greater then n (d) None of these 283. If A and B are two matrices such that rank of and rank of , then (a) rank (AB) = mn (b) rank (AB) rank (A) (c) rank (AB) rank (B) (d) rank (AB) min (rank A, rank B 284. If A is an inevitable matrix and B is a matrix, then (a) rank (AB) = rank (A) (b) rank (AB) = rank (B) (c) rank (AB) > rank (A) (d) rank (AB) > rank (B) 285. If the points and are collinear, then the rank of the matrix will always be less than (a) 3 (b) 2 (c) 1 (d) None of these 286. If A is a matrix such that there exists a square submatrix of order r which is non-singular and every square submatrix of order or more is singular, then (a) rank (A) = r +1 (b) rank (A) = r (c) rank (A) > r (d) rank (A) r +1 287. The rank of the matrix is (a) 1 (b) 2 (c) 3 (d) 4 288. The system of equations of n equations in n unknown has infinitely many solutions if (a) (b) (c) (d) 289. The trace of skew symmetric matrix of order is (a) 0 (b) 1 (c) n (d) 290. If and ,then equals (a) (b) (c) (d) 291. The construction of matrix A whose element is given by is (a) (b) (c) (d) None of these 292. If A is a square matrix of order n such that its elements are polynomial in x and its r-rows become identical for , then (a) is a factor of (b) is a factor of (c) is a factor of (d) is a factor of 293. If is a scalar matrix of order such that for all i, then trace of A is equal to (a) nk (b) (c) (d) None of these