**We are given that,**

A and B are square matrices of the order 3 × 3.

We need to check whether (AB)^{2} = A^{2}B^{2} is true or not.

Take (AB)^{2}.

(AB)^{2} = (AB)(AB)

**[∵ A and B are of order (3 × 3) each, A and B can be multiplied; A and B be any matrices of order (3 × 3)]**

⇒ (AB)^{2} = ABAB

[∵ (AB)(AB) = ABAB]

⇒ (AB)^{2} = AABB

[∵ ABAB = AABB; as A can be multiplied with itself and B can be multiplied by itself]

⇒ (AB)^{2} = A^{2}B^{2}

So, note that, (AB)^{2} = A^{2}B^{2} is possible.

But this is possible if and only if BA = AB.

And BA = AB is always true whenever A and B are square matrices of any order. And for BA = AB,

**(AB)**^{2} = A^{2}B^{2}