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Show that the matrix $$A =\begin{bmatrix} -8& 5\\ 2 & 4\end{bmatrix}$$ satisifies the equation $$A^{2} + 4A - 42I = 0$$ and hence find $$A^{-1}$$.

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Show that the matrix $$A =\begin{bmatrix} -8& 5\\ 2 & 4\end{bmatrix}$$ satisifies the equation $$A^{2} + 4A - 42I = 0$$ and hence find $$A^{-1}$$.
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