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.
