Itt egy 3x3-as mátrix.
\( A = \begin{pmatrix} a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33} \end{pmatrix} \)
Adjungáltja pedig ez lesz.
\( adj(A) = \begin{pmatrix} + \det{ \begin{pmatrix} a_{22} & a_{23} \\ a_{32} & a_{33} \end{pmatrix} } & - \det{ \begin{pmatrix} a_{21} & a_{23} \\ a_{31} & a_{33} \end{pmatrix} } & + \det{ \begin{pmatrix} a_{21} & a_{22} \\ a_{31} & a_{32} \end{pmatrix} } \\ - \det{ \begin{pmatrix} a_{12} & a_{13} \\ a_{32} & a_{33} \end{pmatrix} } & + \det{ \begin{pmatrix} a_{11} & a_{13} \\ a_{31} & a_{33} \end{pmatrix} } & - \det{ \begin{pmatrix} a_{11} & a_{12} \\ a_{31} & a_{32} \end{pmatrix} } \\ + \det{ \begin{pmatrix} a_{12} & a_{13} \\ a_{22} & a_{23} \end{pmatrix} } & - \det{ \begin{pmatrix} a_{11} & a_{13} \\ a_{21} & a_{23} \end{pmatrix} } & + \det{ \begin{pmatrix} a_{11} & a_{12} \\ a_{21} & a_{22} \end{pmatrix} } \end{pmatrix}^T \)
