Let A and B be square matrices
Question:

Let A and B be square matrices of the order 3 × 3. Is (AB)2 = A2 B2 ? Give reasons.

Solution:

As, A and B be square matrices of order 3 x 3.

We have, (AB)2 = AB . AB

= A(BA)B

= A(AB)B [If AB = BA]

= AABB

= A2B2

Thus, (AB)2 = A2B2 is true only if AB = BA.