Eigenvalues · Superchallenge problem

Let $A = \begin{pmatrix}1 & 2\\2 & 1\end{pmatrix}$, $B = \begin{pmatrix}0 & 1\\1 & 0\end{pmatrix}$, and let $M$ be the $6\times 6$ block matrix $M = \begin{pmatrix}A & B & B\\B & A & B\\B & B & A\end{pmatrix}$. Find $\det(M + I)$.