Question

prove this Matrix question​

Answer 1

$\large \color{red} \bold{Given} \\ \\ \sf A \: = \: \begin{gathered}\left[\begin{array}{ccc} 1&0&0 \\ 1&0&1 \\ 0&1&0\end{array}\right]\end{gathered} \\ \\ \color{lime} \bold{To \: find \: {A}^{50} } \\ \\ \sf \: {A}^{50} \: = \: 50 \: \times \: \begin{gathered}\left[\begin{array}{ccc} 1&0&0 \\ 1&0&1 \\ 0&1&0\end{array}\right]\end{gathered} \\ \\ \sf \: {A}^{50} \: = \begin{gathered}\left[\begin{array}{ccc} 1\: \times \: 50&0\: \times \: 50&0\: \times \: 50 \\ 1\: \times \: 50&0\: \times \: 50&1\: \times \: 50 \\ 0\: \times \: 50&1\: \times \: 50&0\: \times \: 50\end{array}\right]\end{gathered} \: \\ \\ \sf \: {A}^{50} \: = \: \begin{gathered}\left[\begin{array}{ccc} 50&0&0 \\ 50&0&50 \\ 0&50&0\end{array}\right]\end{gathered}$