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Inverse of a Matrix

If A2-A+I=0...

Question

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

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 A $I - A$
$A^{2} - A + I = 0$

Multiplying $= A^{- 1} (0)$

$A^{- 1} (A^{2} - A = I) = A^{- 1} (0)$

$A - I + A^{- 1} = 0$

$A^{- 1} = - (A - I)$

$A^{- 1} = I - A$ .

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Similar questions

A^{2} - A + I = 0

, then the inverse of A is
(a) A⁻²
(b) A + I
(c) I − A
(d) A − I

I

A^{2} - A + I = 0

, then the inverse

o f A

A^{2} - A + I = 0

, then the inverse of the matrix

A

A^{2} - A + I = 0

A^{- 1}

A^{2} + A - I = 0

A^{- 1}

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