Q38 of 307 Page 6

If A is a matrix of order m × n and B is a matrix such that AB^T and B^TA are both defined, then the order of matrix B is

Let &

As AB’, is a defined matrix, {Given}

So n = q

BA’ is also a defined matrix, {Given}

So, p = m

Hence order of B is m × n.

Option (D) is the answer.

If A is a square matrix such that A² = I, then (A – I)³ + (A + I)³ – 7A is equal to

If A and B are two matrices of order 3 × m and 3 × n respectively and m = n, then the order of 5A – 2B is

If A and B are matrices of the same order, then AB^T – B^TA is a

If matrix , where , then A² is equal to

If A is a matrix of order m × n and B is a matrix such that ABT and BTA are both defined, then the order of matrix B is