Adjugate Matrix/Examples/3 x 3

Example of Adjugate Matrix
Let $\mathbf A$ be the square matrix of order $3$:


 * $\mathbf A = \begin {pmatrix} a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33} \end {pmatrix}$

Let $A_{ij}$ denote the cofactor of element $a_{ij}$.

Then the adjugate matrix of $\mathbf A$ is:


 * $\adj {\mathbf A} = \begin {pmatrix} A_{11} & A_{21} & A_{31} \\ A_{12} & A_{22} & A_{23} \\ A_{13} & A_{23} & A_{33} \end {pmatrix}$