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Q.

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

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a

$A - I$

b

$A + I$

c

$A^{- 2}$

d

$I - A$

answer is C.

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Detailed Solution

$A^{2} - A + I = 0 Or I = A - A^{2} \begin{array}{l} {IA}^{- 1} = {AA}^{- 1} - A^{2} A^{- 1} \\ A^{- 1} = I - A \end{array}$

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