Rule of Sarrus

linear-algebra

Definition

Rule of Sarrus

The number of permutations of a $3\times 3$ square matrix is $3!=6$. The rule of Sarrus states that the determinant of a $3\times 3$ square matrix is given by:

$$\begin{array}{rl}\left|\begin{array}{ccc}{a}_{11}& a_{12}& a_{13}\\ a_{21}& a_{22}& a_{23}\\ a_{31}& a_{32}& a_{33}\end{array}\right|=& a_{11}{a}_{22}{a}_{33}+a_{12}{a}_{23}a31+a_{13}{a}_{21}{a}_{32}\\ & -a_{13}{a}_{22}{a}_{31}-a_{12}{a}_{21}{a}_{33}-a_{11}{a}_{23}{a}_{32}\end{array}$$