Hello,
Use det(XY)=det(X)det(Y).
Find c such that det(AB^{-1}+cE)=0. -c is the eigenvalue of AB^{-1}.
Bye.
Let A and B be nxn matrices over the field of complex numbers.
How would i show that if B is invertible, then there exists a scalar c in C such that A+cB is not invertible?
i was examining det(A+cB) as given by hints but could not reach a solution.