II.—General Theorems on Determinants

Extract

The rows of a determinant of the n^th order having been separated into two sets, one containing the first p rows and the other the rest, if each minor of the p^th degree formed from the first set be multiplied by a minor, called its complementary, formed from the second set, and the result have its sign chosen in accordance with a certain law, it is well known as an elementary theorem that the aggregate of the products thus obtained is equal to the original determinant.