The recurrence $a_n = 2a_{n-1} + 3a_{n-2}$ can be expressed in matrix form as: $\begin{pmatrix} a_n \\ a_{n-1} \end{pmatrix} = \begin{pmatrix} 2 & 3 \\ 1 & 0 \end{pmatrix} \begin{pmatrix} a_{n-1} \\ a_{n-2} \end{pmatrix}$

Which is the characteristic polynomial of the coefficient matrix $A = \begin{pmatrix} 2 & 3 \\ 1 & 0 \end{pmatrix}$?