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Definition of Relations

If A2-A+I=0...

Question

If $A^{2} - A + I = 0$ , then the inverse of the matrix $A$ is

A - I

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I - A

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A + I

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A

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Solution

The correct option is A $I - A$
Given, $A^{2} - A + I = 0$
$\Rightarrow A^{2} - A = - I$
$\Rightarrow A^{2} A^{- 1} - A A^{- 1} = - I A^{- 1}$
$\Rightarrow A - I = - A^{- 1}$
$\Rightarrow A^{- 1} = I - A$

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