Let M(n) be the time to multiply two n × n matrices, and let D(n) denote the time required to find the determinant of an n × n matrix. Show that multiplying matrices and computing the determinant have essentially the same difficulty: an M(n)-time matrix-multiplication algorithm implies an O(M(n))-time determinant algorithm, and a D(n)-time determinant algorithm implies an O(D(n))-time matrix-multiplication algorithm.