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Question

If A3=0 then 1+A+A2 is equal to

A
I + A
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B
(I+A)1
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C
I - A
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D
(IA)1
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Solution

The correct option is D (IA)1
since the eigenvalue of matrix A is zero

(IA) is invertible we have

(IA)(I+A+A2)=IA3=I0=I

(IA)(I+A+A2)=I

I+A+A2=(IA)1

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