Determinant

2D matrix:

$$\det A=|A|=\left|\begin{array}{cc}a& b\\ c& d\end{array}\right|=ad-bc$$

The determinant of a matrix $[A]$ is a single value.

$$\begin{array}{rl}A& =\left[\begin{array}{ccc}{a}_{11}& a_{12}& a_{13}\\ a_{21}& a_{22}& a_{23}\\ a_{31}& a_{32}& a_{33}\end{array}\right]\\ D& =|A|=\left[\begin{array}{ccc}{a}_{11}& a_{12}& a_{13}\\ a_{21}& a_{22}& a_{23}\\ a_{31}& a_{32}& a_{33}\end{array}\right]\\ & =a_{11}(a_{22}{a}_{33}-a_{23}{a}_{32})-a_{12}(a_{21}{a}_{33}-a_{23}{a}_{31})+a_{13}(a_{21}{a}_{32}-a_{22}{a}_{31})\end{array}$$