Matrix Determinant of Product
Result
It happens that matrix multiplication and the operation of taking the determinant commute. In other words, the determinant of a product of two real matrices is the product of the determinant of each matrix.
Suppose $A \in \R ^{m \times n}$ and $B \in
\R ^{n \times p}$. Then
\[ \det(AB) = \det(A) \det(B) \]