Determinants

The symbol $A=\left|\begin{matrix}a_{11}&a_{12}&a_{13}\\a_{21}&a_{22}&a_{23}\\a_{31}&a_{32}&a_{33}\end{matrix}\right|$ is a determinant of third order that consists of nine numbers arranged in three rows and three columns.
By definition, the value of a determinant of third order is given by:

|A| = a₁₁a₂₂a₃₃+a₁₃a₂₁a₃₂+a₁₂a₂₃a₃₁-a₁₃a₂₂a₃₁-a₁₂a₂₁a₃₃-a₁₁a₂₃a₃₃

and is called the expansion of the determinant.

To remember easily, you can use:

Express the value of the determinant:

5	-5	-5
5	-1	4
1	-3	-1