For any 3 × 3 matrix M , let | M | denote the determinant of M . Let I be the 3 × 3…
Mathematics · JEE Advanced · NTA Exams — Matrices and Determinants
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?
G = (I – EF)–1, then which of the following statements is (are) TRUE?
- |FE| = |I – FE| |FGE|
- (I – FE) (I + FGE) = I
- EFG = GEF
- (I – FE) (I – FGE) = I
Answer
(D) ( I – FE ) ( I – FGE ) = I
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