The minor M_ij of the entry a_ij in D is the determinant of order n - 1 obtained by deleting the ith row and jth column of D. The cofactor of a_ij is defined by
 

in which the entries in the ith column are the corresponding entries in the ith row of D. The determinant D' is called the transpose of D; it is easily seen that D is then the transpose of D'. For example

are transposes of each other.
 
 

Wednesday, June 10, 1998