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.

Try to diagonalize the matrix. Say we could write $X=PDP^{-1}$ where $D$ is diagonal. Then computation would be easy since $X^{50}=PD^{50}P^{-1}$. 
