Definition:Adjugate 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 $\mathbf C$:
 * $\adj {\mathbf A} = \mathbf C^\intercal$

Also known as
Some sources refer to this as the adjoint matrix of $\mathbf A$.

However, as this term is also used for the Hermitian conjugate, to avoid ambiguity it is recommended that it not be used.

Also see

 * Matrix Product with Adjugate Matrix