This can be proven by taking the determinant of the similarity transformation equation, and using (i) the property of the determinant that \(\det(\mathbf{U}\mathbf{V}) = \det(\mathbf{U})\det(\mathbf{V...This can be proven by taking the determinant of the similarity transformation equation, and using (i) the property of the determinant that \(\det(\mathbf{U}\mathbf{V}) = \det(\mathbf{U})\det(\mathbf{V})\), and (ii) the fact that the determinant of a diagonal matrix is the product of the elements along the diagonal.
