$\begin{bmatrix} a\\\\b\end{bmatrix}\longmapsto \begin{bmatrix}-3&1\\\\0&2\end{bmatrix} \begin{bmatrix} a\\\\b\end{bmatrix}$
Use the characteristic polynomail to find all eigenvalues for the transformation for each eigenvalues $\lambda$ find all eigenvectors with eigenvalues $\lambda$ and find a basis for $E_\lambda$
Here is what I have so far
$\chi_f(x)=\begin{bmatrix}-3-x&1\\\\0&2-x\end{bmatrix}$ $=(-3-x)(2-x)$ so there are two eigenvalues $\lambda=-3$ and $\lambda=2$
I'm not sure how to find a basis for these eigenvalues though