Question

If A and B are matrices and the products AB and BA are both defined, then A and B must be square matrices.

Answer 1

Answer: False

Step-by-step explanation

A counterexample could be that A is 2x5 while B is 5x2.

Both AB and BA are defined for these matrix sizes. Neither A nor B are square.

AB is size 2x2 in this case, while BA is size 5x5 in this case.