If $\mathbf{A}^{-1} = \begin{pmatrix} 2 & 1 \\ 0 & -3 \end{pmatrix}$ and $\mathbf{B}^{-1} = \begin{pmatrix} 0 & 5 \\ -1 & 1 \end{pmatrix},$ then find the inverse of $\mathbf{A} \mathbf{B}.$
In general, $(\mathbf{A} \mathbf{B})^{-1} = \mathbf{B}^{-1} \mathbf{A}^{-1}$ (not $\mathbf{A}^{-1} \mathbf{B}^{-1}$), which is
\[\begin{pmatrix} 0 & 5 \\ -1 & 1 \end{pmatrix} \begin{pmatrix} 2 & 1 \\ 0 & -3 \end{pmatrix} = \boxed{\begin{pmatrix} 0 & -15 \\ -2 & -4 \end{pmatrix}}.\]