Compute the matrix $A^n$, $n$ $\in$ $\mathbb{N}$. Compute $A^n$, $n$ $\in$ $\mathbb{N}$., where $
A=\left[\begin{array}{rr}
2&4\\3&13
\end{array}\right]$.
Hi guys, this is the question, I compute the diagonal matrix of $A$ and obtained this $
D=\left[\begin{array}{rr}
1&0\\0&14
\end{array}\right]$. I need use this result $(M^{-1}BM)^n$ $=$ $M^{-1}B^nM$ to find $A^n$ and I know how to use, but my problem is compute this matrix $M$ how can I compute $M$?

Another way to compute $f(A)$ (where $A$ is a matrix, and in your case $f(x)=x^N$) is to use: 
\begin{equation}
f(A) = \frac{1}{2\pi i}\oint  f(z) (z-A)^{-1} \; dz 
\end{equation}
where the contour encloses all the poles of the matrix $(z-A)^{-1}$.
Sounds complicated, but it is very straightforward.
