The adjugate matrix of a square matrix 
is the transpose of its matrix
of cofactors. If 
is obtained by deleting row 
and column 
from 
, its cofactor is
 |
(1)
|
and the adjugate matrix is
 |
(2)
|
The adjugate matrix is also called the classical adjoint. It satisfies
 |
(3)
|
where 
is the identity matrix. If 
has a matrix inverse, then
 |
(4)
|
The cofactor definition remains valid when 
is a singular matrix. For
a 
matrix,
![adj[a b; c d]=[d -b; -c a].](/images/equations/AdjugateMatrix/NumberedEquation5.svg) |
(5)
|
The adjugate matrix is implemented in the Wolfram Language as Adjugate[A].
