Question

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

(a) m × n
(b) n × n
(c) n × m
(d) m × n

Disclaimer: option (a) and (d) both are the same.

Answer 1

Since, AB^T and B^TA are both defined.

And, order of A is m × n. So, Order of B^T must be n × m.

Thus, order of matrix B is m × n.

Hence, the correct option is (d).