If $A^{2} - A + I = 0$ , find the inverse.

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A^{2} - A + I = 0

, find the inverse.

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Text solutionVerified

A^{2} - A + I = 0

pre multiply by

A^{- 1}

A^{- 1} A^{2} - A^{- 1} A + A^{- 1} I = 0

A - I + A^{1} = 0

A^{- 1} = I - A

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