A square matrix is called a permutation matrix if each row and each column contains exactly one entry 1, with all other entries being 0. An example is $$P = \left[\begin{array}{ccc} 1 &0 &0\cr 0 &0 &1\cr 0 &1 &0 \end{array}\right].$$ Find the determinant of this matrix.
$\det(P)=$ .