Q.

If A2=A , the (I+A)4  equals

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a

I+15A

b

I+7A

c

I+8A

d

I+11A

answer is A.

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Detailed Solution

As I  and A  commute, we can apply binomial theorem to expand (I+A)4 . We have (I+A)4=I+4A+6A2+4A3+A4 But A3=A2=A, A4=A3=A ∴     (I+A)4=I+4A+6A+4A+A=I+15A
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If A2=A , the (I+A)4  equals