Question

Let A be a matrix of order m × n and B is a matrix such that A^TB and BA^T are defined. Then, the order of B is ______.

Options

• m × m

• n × n

• m × n

• n × m

Answer 1

Let A be a matrix of order m × n and B is a matrix such that A^TB and BA^T are defined. Then, the order of B is m × n.

Explanation:

Given, order of matrix A = m × n 

Then, order of matrix A^T = n × m

Let order of matrix B = p × q

A^T.B is defined

So, columns of A^T = Rows of B

m = p

Again, B.A^T is defined So, columns of B = Rows of AT

q = n

Then, order of B = m × n