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Question

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

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Solution

Since, A and B are square matrices such that AB = BA.
∴ (A+B)2 = (A+B).(A+B)
= A2 + AB + BA + B2
= A2 + AB + AB + B2

[∴ AB = BA]

= A2 + 2AB + B2

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