Let A and B be k x k matrices and let:

$\displaystyle M = \left( \begin{array}{rr} O & B \\ A & O \end{array}\right)$

Show that $\displaystyle det(M)=(-1)^kdet(A)det(B)$

How would I go about this? For example, are the rules for finding the determinants of block matrices similar to finding the determinants of normal matrices (ie multiplying diagonally and summing the result)?

Any help welcome.