Show that the determinant of a matrix A is equal to the product of its eigenvalues λi.
So I'm having a tough time figuring this one out. I know that I have to work with the characteristic polynomial of the matrix det(A−λI). But, when considering an n×n matrix, I do not know how to work out the proof. Should I just use the determinant formula for any n×n matrix? I'm guessing not, because that is quite complicated. Any insights would be great.