\[\det[a_{jk}]=\begin{vmatrix}a_{11}&a_{12}&a_{13}\\
a_{21}&a_{22}&a_{23}\\
a_{31}&a_{32}&a_{33}\end{vmatrix}=a_{11}\begin{vmatrix}a_{22}&a_{23}\\
a_{32}&a_{33}\end{vmatrix}-a_{12}\begin{vmatrix}a_{21}&a_{23}\\
a_{31}&a_{33}\end{vmatrix}+a_{13}\begin{vmatrix}a_{21}&a_{22}\\
a_{31}&a_{32}\end{vmatrix}=a_{11}a_{22}a_{33}-a_{11}a_{23}a_{32}-a_{12}a_{21}a%
_{33}+a_{12}a_{23}a_{31}+a_{13}a_{21}a_{32}-a_{13}a_{22}a_{31}.\]