Eigenvalues · Challenge problem

Let $A = \begin{pmatrix}5 & 3\\1 & 3\end{pmatrix}$ and let $M$ be the $4\times 4$ block matrix $M = \begin{pmatrix}0 & A\\I & I\end{pmatrix}$, where $0$ and $I$ are the $2\times 2$ zero and identity matrices. Find the largest eigenvalue of $M$.