The determinant of a matrix M is written as either $|{\bf~M}|$ or det( M ).

• The determinant of a 2x2 matrix is the area scale-factor.
• The determinant of a 3x3 matrix is the volume scale-factor.
The determinant of a 2x2 matrix $\left[\begin{matrix}a&b\\c&d\end{matrix}\right]$ is $\left|\begin{matrix}a&b\\c&d\end{matrix}\right|=ad-bc$

Determinants can be used to find the vector cross product.