Linear Transformations · Superchallenge problem

Let $A = \begin{pmatrix}1 & 2\\3 & 4\end{pmatrix}$ and $B = \begin{pmatrix}2 & 1\\1 & 1\end{pmatrix}$. The map $T(X) = AXB$ is a linear transformation of the $4$-dimensional space $M_2$ of real $2\times 2$ matrices. Find $\det T$.