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Question
Let A and B be square matrices of the order 3 × 3. Is (AB)2 = A2B2? Give reasons.
Solution
As, A and B be square matrices of order 3 × 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.
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