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 .