Not to be confused with Definition:Adjoint Matrix.

## Definition

Let $R$ be a commutative ring with unity.

Let $\mathbf A \in R^{n \times n}$ be a square matrix of order $n$.

Let $\mathbf C$ be its cofactor matrix.

The adjugate matrix of $\mathbf A$ is the transpose of $\mathbf C$:

$\adj {\mathbf A} = \mathbf C^\intercal$