Questions:

54. The rank of a matrix is defined as the maximum number of : (a) linearly independent rows of a matrix (b) linearly independent columns of a matrix (c) both a & b (d) neither a nor b 55. A diagonal matrix in which all the diagonal elements are equal is called: (a) unit matrix (b) null matrix (c) scalar matrix (d) triangular matrix 56. If A is an mxn matrix, and B is an nxk matrix , then product AB is of order : (a) mxn (b) nxk (c) nxn (d) mak 57. A square matrix A is said to be orthogonal if : (a) AAT = A2 (b) AAT =1 = ATA (c) A + AT = A +A (d) none of these 58. Let A and B be skew symmetric matrix, then AB is symmetric if and only if : (a) AB = BA (b) AB 0 (C) A = ET (d) A = -BT 59. A square matrix B is orthogonal if : (a) B = -BT (b) B = BT (C) BY = B-1 (d) BT = -B-1 60. If A and B are square matrices such that AB=BA , then A and B are called : (a) anti commutative (b) commutative (c)associative (d) periodic 61. Two matrices A and B are said to be conformable for multiplication only if : (a) The number of rows of A is equal to the number of rows of B (b) The number of columns of A is equal to the number of columns of B (c) The number of rows of A is equal to the number of columns of B (d) The number of columns of A is equal to the number of rows of B 62. Matrix addition is: (a) Commutative (b) Associative (c) Have additive identity (d) all the above. 63. Transpose of a matrix A of order mxn is of order: (a) mxm (b) nxn (c) nxm (d) none of these. 64. Determinants are possible only when : (a) number of rows > number of columns. (b) number of rows