Diagonalization & Matrix Powers · Easy problem

A $2\times 2$ matrix $A$ satisfies $A\begin{pmatrix}1\\-2\end{pmatrix} = -\begin{pmatrix}1\\-2\end{pmatrix}$ and $A\begin{pmatrix}1\\1\end{pmatrix} = 3\begin{pmatrix}1\\1\end{pmatrix}$. Find the first entry of $A^4\begin{pmatrix}2\\-1\end{pmatrix}$.