Calculating determinant of a block diagonal matrix Given an $m \times m$ square matrix $M$:
$$
M = \begin{bmatrix}
A & 0 \\
0 & B
\end{bmatrix}
$$
$A$ is an $a \times a$ and $B$ is a $b \times b$ square matrix; and of course $a+b=m$. All the terms of A and B are known.
Is there a way of calculating determinant of $M$ by determinants of (or any other useful data from) of $A$ and $B$ sub-matrices?

Hint: It's easy to prove that
$$\det M=\det A\det B$$
