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Matrices and Determinants question

2021 · Shift 1 · Q33

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PYQ Library
JEE Advanced
Mathematics
Matrices and Determinants
2021 · Shift 1 · Q33

Matrices and Determinants question

2021 · Shift 1 · Q33

JEE AdvancedMathematicsMatrices and DeterminantsMultiple correct+4 / −2

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

-

EF) is invertible. If G = (I

-

EF)

-

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

A
| FE | = | I $-$ FE| | FGE |
B
(I $-$ FE)(I + FGE) = I
C
EFG = GEF
D
(I $-$ FE)(I $-$ FGE) = I

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