If \( A=\left[\begin{array}{rr}3 & 1 \\ -1 & 2\end{array}\right] \)...

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If \( A=\left[\begin{array}{rr}3 & 1 \\ -1 & 2\end{array}\right] \) and \( I=\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right] \), then find \( \lambda \) so that \( A^{2}=5 A+\lambda I \).
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