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

Since, A and B are square matrices of order

$3 \times 3$.
$\therefore$ $A{B^2} = AB \cdot AB$

$= ABAB$
$= AABB$
$= {A^2}{B^2}$

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