MATHEMATICS · Multi correct · AP · AP Precalculus · Functions with Parameters, Vectors, and Matrices · Functions with Parameters, Vectors, and Matrices
Problem
For any 3×3 matrix M, let ∣M∣ denote the determinant of M. Let I be the 3×3 identity matrix. Let E and F be two 3×3 matrices such that (I−EF) is invertible.
If G=(I−EF)−1, which of the following statements are true?
(A) ∣EF∣=∣I−FE∣
(B) (I−FE)(I+FGE)=I
(C) EFG=GEF
(D) (I−FE)(I−FGE)=I