For any $$3 \times 3$$ matrix M, let $$\mid M \mid$$ denote the determinant of M. Let I be the $$3 \times 3$$ identity matrix. Let E and F be two $$3 \times 3$$ matrices such that $$(I − EF)$$ is invertible. If $$G = (I − EF) − 1$$, then which of the following statements is (are) TRUE ?

A

$$\mid FE \mid = \mid I - FE \mid \mid FGE \mid$$

B

$$(I - FE)(I + FGE) = I$$

C

$$EFG = GEF$$

D

$$(I - FE)(I - FGE) = I$$