Given the system of equations $\begin{pmatrix} a_{n+1} \\ a_n \end{pmatrix} = \begin{pmatrix} 2 & 1 \\ 1 & 0 \end{pmatrix} \begin{pmatrix} a_n \\ a_{n-1} \end{pmatrix}$, what is the trace and determinant of the transition matrix $M$?