Question

Let A and B be square matrices of the order 3 $\times$ 3. Is $(AB{)}^2=A^2{B}^2$ ? Give reasons.

Answer 1

Since, A and B are square matrices of order 3 $\times$ 3.

$A{B}^2$ = AB. AB

= ABAB

=AABB [$\because$ AB = BA]

=$A^2{B}^2$

So, $A{B}^2$ = $A^2{B}^2$ is true when AB = BA