余因子行列
adj  ( A ) = C T = [ + | a 22 a 23 a 32 a 33 | − | a 12 a 13 a 32 a 33 | + | a 12 a 13 a 22 a 23 | − | a 21 a 23 a 31 a 33 | + | a 11 a 13 a 31 a 33 | − | a 11 a 13 a 21 a 23 | + | a 21 a 22 a 31 a 32 | − | a 11 a 12 a 31 a 32 | + | a 11 a 12 a 21 a 22 | ] {\displaystyle \operatorname {adj} (A)=C^{\mathsf {T}}={\begin{bmatrix}+{\begin{vmatrix}a_{22}&a_{23}\\a_{32}&a_{33}\end{vmatrix}}&-{\begin{vmatrix}a_{12}&a_{13}\\a_{32}&a_{33}\end{vmatrix}}&+{\begin{vmatrix}a_{12}&a_{13}\\a_{22}&a_{23}\end{vmatrix}}\\&&\\-{\begin{vmatrix}a_{21}&a_{23}\\a_{31}&a_{33}\end{vmatrix}}&+{\begin{vmatrix}a_{11}&a_{13}\\a_{31}&a_{33}\end{vmatrix}}&-{\begin{vmatrix}a_{11}&a_{13}\\a_{21}&a_{23}\end{vmatrix}}\\&&\\+{\begin{vmatrix}a_{21}&a_{22}\\a_{31}&a_{32}\end{vmatrix}}&-{\begin{vmatrix}a_{11}&a_{12}\\a_{31}&a_{32}\end{vmatrix}}&+{\begin{vmatrix}a_{11}&a_{12}\\a_{21}&a_{22}\end{vmatrix}}\end{bmatrix}}}