If \( A=\left[\begin{array}{rr}2 & -1 \\ -1 & 2\end{array}\right] \) and \( I \) is the identity...

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If \( A=\left[\begin{array}{rr}2 & -1 \\ -1 & 2\end{array}\right] \) and \( I \) is the identity matrix of order 2, then show that \( \mathrm{A}^{2}=4 \mathrm{~A}-3 \mathrm{I} \). Hence, find \( \mathrm{A}^{-1} \)
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