Diagonalization & Matrix Powers · Medium problem

A sequence has $a_0 = 1$, $a_1 = 8$ and $a_{n+1} = a_n + 6a_{n-1}$ for $n \ge 1$. Diagonalize the matrix $\begin{pmatrix}1 & 6\\1 & 0\end{pmatrix}$ that sends $\begin{pmatrix}a_n\\a_{n-1}\end{pmatrix}$ to $\begin{pmatrix}a_{n+1}\\a_n\end{pmatrix}$ to get a closed form for $a_n$, and find $a_6$.