Chapter 2.2, Problem 31E

It can be proved that if a square matrix M is partitioned into block triangular form as

$M=\left[\begin{array}{cc}A& 0\\ C& B\end{array}\right]or\text{ M=}\left[\begin{array}{cc}A& C\\ 0& B\end{array}\right]$

In which A and B are square, then det(M) = det(A) det(B). Use this result to compute the determinants of the matrices in Exercises 31 and 32.

$M=\left[\begin{array}{cccccc}1& 2& 0& 8& 6& -9\\ 2& 5& 0& 4& 7& 5\\ -1& 3& 2& 6& 9& -2\\ 0& 0& 0& 3& 0& 0\\ 0& 0& 0& 2& 1& 0\\ 0& 0& 0& -3& 8& -4\end{array}\right]$