For any 3 \times 3 matrix M, let |M| 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-E F) is invertible. If G=(I-E F)^{-1}, then which of the following statements is (are) TRUE? [JEE Adv 2021 P1]

Matrices and Determinants

Section: Mathematics

Question : 13 of 56

Marks: +1, -0

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, then which of the following statements is (are) TRUE?

[JEE Adv 2021 P1]

|FE|=|I−FE||FGE|
(I−FE)(I+FGE)=I
EFG=GEF
(I−FE)(I−FGE)=I

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