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I have this question, I need to choose the correct answer:

A is a square matrix such that

\[A^{2}+A+I=0\]

a) \[A^{-1}=A\]

b) \[A^{-1}=A^{2}\]

c) It is not possible to say if A is invertible

d) A is not invertible

e) \[A^{-1}=A+I\]

I got that

\[-A^{2}-A=I\]

and thus

\[A(-A-I)=0\]

and thus

\[A^{-1}=(-A-I)\]

and answer which doesn't exist, am I wrong ?

Thanks !