Question

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Answer 1

$A^2= \left[\begin{array}{ccc} 0&5\\1&0\end{array}\right] \left[\begin{array}{ccc} 0&5\\1&0\end{array}\right] =\left[\begin{array}{ccc} 5&0\\0&5\end{array}\right] =5 I_{2}$Deci A^2016=(A^2)^1005=(5$I_{2}$)^1008=5^1008$I_{2}$