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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 $E=\left[\begin{array}{ccc}1 & 2 & 3 \\ 2 & 3 & 4 \\ 8 & 13 & 18\end{array}\right], P=\left[\begin{array}{lll}1 & 0 & 0 \\ 0 & 0 & 1 \\ 0 & 1 & 0\end{array}\right]$ and $F=\left[\begin{array}{ccc}1 & 3 & 2 \\ 8 & 18 & 13 \\ 2 & 4 & 3\end{array}\right]$ If $Q$ is a nonsingular matrix of order $3 \times 3$, then which of the following statements is (are) TRUE ?
Select ALL correct options:
A
$F=P E P$ and $P^2=\left[\begin{array}{lll}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{array}\right]$
B
$\left|\mathrm{EQ}+\mathrm{PFQ}^{-1}\right|=|\mathrm{EQ}|+\left|\mathrm{PFQ}^{-1}\right|$
C
$\left|(E F)^3\right|>|E F|^2$
D
Sum of the diagonal entries of $P^{-1} E P+F$ is equal to the sum of diagonal entries of $E+P^{-1} F P$
✓ Correct! Well done.
✗ Incorrect. Try again or view the solution.
⚠ Partially correct. Some answers are missing.
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