1. The problem statement, all variables and given/known data So I'm working on this proof. Given an n x n (square) matrix, prove that it's determinant is equal to the product of it's singular values. 2. Relevant equations We are given A = U*E*V as a singular value decomposition of A. 3. The attempt at a solution I was thinking that det(A) = det(U) * det(E) * det(V) and since E is the diagonal matrix with singular values on it's diagonal, it's determinant is the product of those singular values. But then what to do about det(U) and det(V)? I guess it's logical that the product of their determinants is 1, but how do I show that?