If \( \mathrm{A}=\left[\begin{array}{ll}3 & -4 \\ 1 & -1\end{array}\right] \), then prove that \...

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If \( \mathrm{A}=\left[\begin{array}{ll}3 & -4 \\ 1 & -1\end{array}\right] \), then prove that \( \mathrm{A}^{n}=\left[\begin{array}{cc}1+2 n & -4 n \\ n & 1-2 n\end{array}\right] \), where \( n \) is any positive
P integer.

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