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If A^3 = 0 then 1 + A + A^2 is equal to

Question

If $A^{3} = 0$ then $1 + A + A^{2}$ is equal to

I + A

(I + A)^{- 1}

I - A

(I - A)^{- 1}

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Benjamin Discussed

A^{3} = 0

then

1 + A + A^{2}

is equal to

11 mins ago

Discuss this question LIVE

11 mins ago

Text solutionVerified

since the eigenvalue of matrix

A

is zero

(I - A)

is invertible we have

(I - A) (I + A + A^{2}) = I - A^{3} = I - 0 = I

(I - A) (I + A + A^{2}) = I

∴ I + A + A^{2} = (I - A)^{- 1}

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