Let be an rowed minor of the th order determinant associated with an matrix in which the rows , , ..., are represented with columns , , ..., . Define the complementary minor to as the rowed minor obtained from by deleting all the rows and columns associated with and the signed complementary minor to to be
(1)

Let the matrix of cofactors be given by
(2)

with and the corresponding rowed minors of and , then it is true that
(3)
