Proving that $\det (M) = \det (A) \det(D-CA^{-1}B)$

Question

So the task is the following:

Be $M\in M_{m\times n}(K)$ a block matrix

$$M = \bigg( \begin{array}{cc} A & B \\ C & D \\ \end{array} \bigg) $$

with $A\in M_m (K)$, $B,C^t\in M_{m\times n}(K)$ and $D\in M_n (K)$ and let $A$ be invertable.

Show that: (a) $\det (M)=\det (A) \det (D-C(A^{-1})B$.

(b) If $m=n$ and $AB=BA$, $\det (M)=\det (DA-CB)$.

Note for (a): Multiplicate $M$ with a proper block matrix.

I am really lost on this one... and would really appreciate any help.