Show that the matrix \( A=\left[\begin{array}{rr}5 & 3 \\ 12 & 7\en...

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Show that the matrix \( A=\left[\begin{array}{rr}5 & 3 \\ 12 & 7\end{array}\right] \) is a root of the equation \( A^{2}-12 A-I=O \).
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