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Transpose of a Matrix

If A and B be...

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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