If A^2 - A + I = 0, then the inverse of A is __________ .

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I − A 	ext{ Given: }A^2 - A + I = O A^{- 1} \left( A^2 - A + I ight) = A^{- 1} O ............. \left[	ext{ multiplying both sides by }A^{- 1} ight] \Rightarrow \left( A^{- 1} A^2 ight) - \left( A^{- 1} A ight) + A^{- 1} I = O ...............\left[ \because A^{- 1} O = O ight] \Rightarrow A - I + A^{- 1} = O ...............\left[ \because A^{- 1} I = A^{- 1} ight] \Rightarrow A^{- 1} = I - A

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