Any row 
and column 
of a determinant being selected, if the element common
to them be multiplied by its cofactor in the determinant,
and every product of another element of the row by another element of the columns
be multiplied by its cofactor, the sum of the results
is equal to the given determinant. Symbolically,
 |  |  |
(1)
|
 |  |  |
(2)
|
where 
,
2, ..., 
;
;
;
and the sign before 
is determined by the formula 
, with 
the total number of permutation
inversions in the suffix and 
.
