[SOLVED] Generalizing the n-th power of a matrix

Question here, I'm interested in generalizing the n-th power of a matrix P, $\displaystyle P^n$. The vector in question is $\displaystyle P=\left(\begin{array}{ccc}1&0&0\\0.2&0.5&0.3\\0&0. 7&0.3\end{array}\right)$

I've found two approaches to doing this, z-transform and Diagonalization but I'm getting conflicting answers with both. What answer are you getting? also, is there a program that can calculate this for any matrix (perhaps a project I could pick up later if not)? Thanks