For the matrix \( A=\left[\begin{array}{rr}1 & -1 \\ 2 & 3\end{array}\right] \), show that \( A^...

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For the matrix \( A=\left[\begin{array}{rr}1 & -1 \\ 2 & 3\end{array}\right] \), show that \( A^{2}-4 A+5 I=O \). Hence, obtain \( A^{-1} \).
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