Determinants & Inverses · Challenge problem

Compute $\det\begin{pmatrix}1 & 0 & 2 & 1\\0 & 1 & 1 & 3\\1 & 2 & 4 & 0\\3 & 1 & 0 & 5\end{pmatrix}$ by treating it as a $2\times2$ block matrix.