Assume that A and B are in M(C). Show that if Bis invertible, then there exists a scalarCE C such that A + cB is not invertible. Hint: First, show that det (A + tB)- det(B) - det (AB+ tl). Next, use...

Extracted text: Assume that A and B are in M(C). Show that if Bis invertible, then there exists a scalarCE C such that A + cB is not invertible. Hint: First, show that det (A + tB)- det(B) - det (AB+ tl). Next, use the fundamental theorem must have a complex eigenvalue A. Conclude that A+ cBis -1 of algebra to argue that the matrix AB not invertible for c= A.