Determinant of a $2\times 2$ block matrix

Let A, B, C, D be non-degenerate matrices of the same dimension. Show that

\[ \operatorname* { d e t } { \left[ \begin{array} { l l } { A } & { B } \\ { C } & { D } \end{array} \right] } = \operatorname* { d e t } \left( A D - B D ^ { - 1 } C D \right) .\tag{1} \]