If \( \mathrm{A}=\left[\begin{array}{ll}1 & 1 \\ 1 & 1\end{array}\right] \), prove that \( \math...
If \( \mathrm{A}=\left[\begin{array}{ll}1 & 1 \\ 1 & 1\end{array}\right] \), prove that \( \mathrm{A}^{n}=\left[\begin{array}{ll}2^{n-1} & 2^{n-1} \\ 2^{n-1} & 2^{n-1}\end{array}\right] \), for all positive integers \( n \).
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