Adjugate Matrix/Examples/3 x 3

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


 * $\mathbf A = \begin {pmatrix} a_{1 1} & a_{1 2} & a_{1 3} \\ a_{2 1} & a_{2 2} & a_{2 3} \\ a_{3 1} & a_{3 2} & a_{3 3} \end {pmatrix}$

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

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


 * $\adj {\mathbf A} = \begin {pmatrix} A_{1 1} & A_{2 1} & A_{3 1} \\ A_{1 2} & A_{2 2} & A_{3 2} \\ A_{1 3} & A_{2 3} & A_{3 3} \end {pmatrix}$