Question: If A and B are n n matrices, show that: (a) AB = BA if and only if (A + B)2 = A2 +

If A and B are n × n matrices, show that:
(a) AB = BA if and only if
(A + B)2 = A2 + 2AB + B2.
(b) AB = BA if and only if
(A + B)(A - B) = (A - B)(A + B).

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