A \[3\times 3\] can be reprentated as \[ \begin{vmatrix}a_{11}&a_{12}&a_{13}\\a_{21}&a_{22}&a_{23}\\a_{31}&a_{32}&a_{33}\end{vmatrix}\] can be evaluated by finding its cofactor along any row or any column.
Expansion through 1st row \[ \Delta \]=\[a_{11}\]\[ \begin{vmatrix}a_{22}&a_{23}\\a_{32}&a_{33}\end{vmatrix}\]-\[ a_{12}\begin{vmatrix}a_{21}&a_{23}\\a_{31}&a_{33}\end{vmatrix}\]+\[ a_{13}\begin{vmatrix}a_{21}&a_{22}\\a_{31}&a_{32}\end{vmatrix}\]
\[ \Delta \]=\[ a_{11}(a_{22}a_{33}-a_{32}a_{23})-a_{12}(a_{21}a_{33}-a_{31}a_{23})+a_{13}(a_{21}a_{32}-a_{31}a_{22})\]
Note- Expansion through any row or column gives thge same value.
