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Question
Show that if A and B are square matrices such that AB = BA, then (A + B)2 = A2 + 2AB + B2.
Solution
Given, A and B are square matrices such that AB = BA.
So, (A + B)2 = (A + B) · (A + B)
= A2 + AB + BA + B2
= A2 + AB + AB + B2 ......[Since, AB = BA]
= A2 + 2AB + B2
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