I need to calculate $x^{50}$ $x=\begin{pmatrix}1&0&0\\1&0&1\\0&1&0\end{pmatrix}$, I need to calculate $x^{50}$
Could anyone tell me how to proceed?
Thank you.

Evaluate the first few powers and guess
$\begin{pmatrix}1&0&0\\1&0&1\\0&1&0\end{pmatrix}^{2n}$ = $\begin{pmatrix}1&0&0\\n&1&0\\n&0&1\end{pmatrix}$, proof by induction. Then $x^{50}=\begin{pmatrix}1&0&0\\25&1&0\\25&0&1\end{pmatrix}$.
