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Inverse of a Matrix

If A2-A+I=0...

Question

$I$ f $A^{2} - A + I = 0$ , then the inverse $o f A$ is

A

I - A

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B

A-I

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C

A

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D

A + I

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Solution

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

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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

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

A^{2} - A + I = 0

, then the inverse of the matrix

A

A = [\begin{matrix} 0 & - 1 1 & 0 \end{matrix}],

then which one of the following statements is not correct ?

A = [\begin{matrix} 1 & 0 & - 3 \\ 2 & 1 & 3 \\ 0 & 1 & 1 \end{matrix}]

, then verify that A² + A = A(A + I), where I is the identity matrix.

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