Let A and B be n*n matrices. Show that AB and BA have the same eigenvalues.
(Hint: Consider separately the two cases (i) B is invertible, and
(ii) B is not invertible.
Let A and B be n*n matrices. Show that AB and BA have the same eigenvalues.
(Hint: Consider separately the two cases (i) B is invertible, and
(ii) B is not invertible.