Let (shown in matrix blocks) $M=\big( \begin{smallmatrix} A & B \\ C & D \end{smallmatrix} \big)$ a square matrix such that $A$ is invertible and $D$ is a square matrix. I have to prove that

$$\det(M)=\det(A)\cdot \det(D-C·A^{-1}·B)$$

I also have an indication to use it:  

Consider previously these cases:
\begin{align\*}
A\_1 &= \begin{pmatrix} A & 0 \\ 0 & I \end{pmatrix},\\
A\_2 &= \begin{pmatrix} I & 0 \\ 0 & D \end{pmatrix},\\
A\_3 &= A\_1·A\_2,\\
A\_4 &= \begin{pmatrix} I & A^{-1}·B \\ 0 & I \end{pmatrix},\text{ and}\\
A\_5 &= A\_3\cdot A\_4.
\end{align\*} 

The problem is difficult in general for me and I don't even know how to use the indication.