If \( A=\left[\begin{array}{ll}3 & -2 \\ 4 & -2\end{array}\right] \...

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If \( A=\left[\begin{array}{ll}3 & -2 \\ 4 & -2\end{array}\right] \), find the value of \( \lambda \) so that \( A^{2}=\lambda A-2 I \). Hence, find \( A^{-1} \).
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