Question

What is the meaning of determinants?

Answer 1

The determinant is a quantity obtained by the addition of products of square matrix elements.

The determinant of a matrix $A$ is denoted by $\left|A\right|$ or $det\left(A\right)$.

Example: The determinant of a $3\times 3$ matrix $A=\left[\begin{array}{ccc}{a}_{11}& a_{12}& a_{13}\\ a_{21}& a_{22}& a_{23}\\ a_{31}& a_{32}& a_{33}\end{array}\right]$ is,

$\left|A\right|=a_{11}\left(a_{22}{a}_{33}-a_{23}{a}_{32}\right)-a_{12}\left(a_{21}{a}_{33}-a_{23}{a}_{31}\right)+a_{13}\left(a_{21}{a}_{32}-a_{22}{a}_{31}\right)$