Diagonalization & Matrix Powers · Medium problem

A $2\times 2$ matrix $A$ has eigenvalue $2$ with eigenvector $\begin{pmatrix}1\\1\end{pmatrix}$ and eigenvalue $-1$ with eigenvector $\begin{pmatrix}1\\2\end{pmatrix}$. Find the entry in row 1, column 2 of $A^{-1}$.