IMC 1997 Problem 8

Let $M \in GL_{2n}(K)$ , represented in block form as $$M = \left[ \begin{array}{cc} A & B C & D \end{array} \right] , M^{-1} = \left[ \begin{array}{cc} E & F G & H \end{array} \right]$$ Show that $\det M.\det H=\det A$ .