A recurrence relation is represented by the matrix form $\begin{pmatrix} a_{n} \\ a_{n-1} \end{pmatrix} = \begin{pmatrix} 3 & -2 \\ 1 & 0 \end{pmatrix} \begin{pmatrix} a_{n-1} \\ a_{n-2} \end{pmatrix}$. What is the characteristic equation of this system?