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JEE Advanced 2021
Paper-1
Multiple correct answers - Select all that apply
Question
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 $(1-E F)$ is invertible. If $G=(1-E F)^{-1}$, then which of the following statements is (are) TRUE ?
Select ALL correct options:
A
$|F E|=|I-E F||F G E|$
B
$(1-\mathrm{FE})(1+\mathrm{FGE})=1$
C
$\mathrm{EFG}=\mathrm{GEF}$
D
$(1-F E)(1-F G E)=1$
✓ Correct! Well done.
✗ Incorrect. Try again or view the solution.
⚠ Partially correct. Some answers are missing.
Solution
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JEE Advance
Mathematics
Hard
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