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

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