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A square non-singular matrix A satisfies $A^{2} - A + 2 I = 0, then A^{- 1} =$

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I – A

$\frac{1}{2} (I - A)$

I + A

$\frac{1}{2} (I + A)$

answer is B.

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Detailed Solution

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

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