The calculator will find the adjoint (adjugate, adjunct) matrix of the given square matrix, with steps shown.

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Find the adjugate matrix of $\left[\begin{array}{ccc}1 & 2 & 3\\4 & 5 & 6\\7 & 8 & 9\end{array}\right]$.

## Solution

The adjugate, classical adjoint, or adjunct of a square matrix is the transpose of its cofactor matrix.

The cofactor matrix is $\left[\begin{array}{ccc}-3 & 6 & -3\\6 & -12 & 6\\-3 & 6 & -3\end{array}\right]$ (for steps, see cofactor matrix calculator).

The transpose of the cofactor matrix is $\left[\begin{array}{ccc}-3 & 6 & -3\\6 & -12 & 6\\-3 & 6 & -3\end{array}\right]$ (for steps, see matrix transpose calculator).

The adjugate matrix is $\left[\begin{array}{ccc}-3 & 6 & -3\\6 & -12 & 6\\-3 & 6 & -3\end{array}\right]$A.