Q.

If A and B are two matrices such that AB = B and BA = A, then A2 + B2 =

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a

2AB

b

2BA

c

A+B

d

AB

answer is C.

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Detailed Solution

We have,A2 + B2 = AA + BB = A (BA) + B (AB)                           (∵ AB = B and BA = A)= (AB) A + (BA) B= BA + AB = A + B                          (∵ AB = B and BA = A)
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If A and B are two matrices such that AB = B and BA = A, then A2 + B2 =