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Question
Let A and B be square matrices of the order 3 × 3. Is (AB)2 = A2 B2? Give reasons.
Solution
Yes, (AB)2 = A2 B2 if AB = BA.
If AB = BA, then
(AB)2 = (AB)(AB)
= A(BA)B (associative law)
= A(AB)B
= A2 B2
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