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Inverse of a Matrix

If A3 = 0, th...

Question

If $A^{3} = 0$ , then $I + A + A^{2}$ equals

A

I - A

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B

(I - A)^{- 1}

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C

(I + A)^{- 1}

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D

n o n e o f t h e s e

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Solution

The correct option is B $(I - A)^{- 1}$
$A^{3} = 0 (I + A + A^{2}) (I - A) = I - A^{3} = 1 ∴ I + A + A^{2} = (I - A)^{- 1}$

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