A,BA, BA,B non-singular of the same order, C=BAB−1C = B A B^{-1}C=BAB−1. For scalar λ\lambdaλ, det(C+λI)\det(C + \lambda I)det(C+λI) equals
detA\det AdetA
detB\det BdetB
det(A+λI)\det(A + \lambda I)det(A+λI)
det(B+λI)\det(B + \lambda I)det(B+λI)
