 If "S" is a subset of {1, ..., "n"} with "m" elements, we write "AS" for the "m"×"m" matrix whose columns are those columns of "A" that have indices from "S".Similarly, we write "BS" for the "m"×"m" matrix whose "rows" are those rows of "B" that have indices from "S".Then the determinant of the matrix product of "A" and "B" satisfies the identity
where the sum extends over all possible subsets "S" of {1, ..., "n"} with "m" elements.