If \( A=\left[\begin{array}{rr}-1 & -1 \\ 2 & -2\end{array}\right] ...

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If \( A=\left[\begin{array}{rr}-1 & -1 \\ 2 & -2\end{array}\right] \), show that \( A^{2}+3 A+4 I_{2}=O \) and hence find \( A^{-1} \).
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