A square nonsingular matrix satisfies $A^{2} - A + 2 I = 0, t h e n A^{- 1} =$

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(I+A)/2

I+A

I-A

(I-A)/2

answer is B.

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Detailed Solution

$\begin{array}{l} A^{2} - A + 2 I = 0 \\ \Rightarrow A (A - I) = - 2 I \\ \Rightarrow A (I - A) = 2 I \\ \Rightarrow A (\frac{I - A}{2}) = I \\ \Rightarrow A^{- 1} = (\frac{I - A}{2}) \end{array}$

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