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Question
If A and B are square matrices of the same order such that AB = BA, then show that (A + B)2 = A2 + 2AB + B2.
Solution
(A + B)2 = (A + B)(A + B)
= A2 + AB + BA + B2
= A2 + 2AB + B2 (∵ AB = BA)
Hence, (A + B)2 = A2 + 2AB + B2.
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