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If matrix A i...

Question

If matrix $A$ is non-singular and satisfies $A^{2} - A + I = O,$ then the inverse of $A$ is equal to

A

A^{- 2}

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B

A + I

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C

I - A

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D

A - I

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Solution

The correct option is C $I - A$
Given: $A^{2} - A + I = O$
$\Rightarrow I = A - A^{2}$
$\Rightarrow I A^{- 1} = A A^{- 1} - A^{2} A^{- 1}$
$\Rightarrow A^{- 1} = I - A \cdot A A^{- 1} = I - A I$
$\Rightarrow A^{- 1} = I - A$

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