Question:
Show that the $A=\left[\begin{array}{ccc}1 & 0 & -2 \\ -2 & -1 & 2 \\ 3 & 4 & 1\end{array}\right]$ satisfies the equation $A^{3}-A^{2}-3 A-I=O$, and hence find $A^{-1}$.
Solution:
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