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If $A^2-A+I=0$, then $A^{-1}=$
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Verified Answer
The correct answer is:
$I-A$
$A^2-A+I=0$
$\Rightarrow \quad I=A-A^2 \Rightarrow I=A(I-A)$
$\Rightarrow A^{-1} I=A^{-1}(A(I-A)) \Rightarrow A^{-1}=I-A$.
$\Rightarrow \quad I=A-A^2 \Rightarrow I=A(I-A)$
$\Rightarrow A^{-1} I=A^{-1}(A(I-A)) \Rightarrow A^{-1}=I-A$.
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