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JEE ADVANCE 2019
paper 1
Multiple correct answers - Select all that apply
Question
Let $M=\left[\begin{array}{lll}0 & 1 & a \\ 1 & 2 & 3 \\ 3 & b & 1\end{array}\right]$ and $\operatorname{adj} M=\left[\begin{array}{ccc}-1 & 1 & -1 \\ 8 & -6 & 2 \\ -5 & 3 & -1\end{array}\right]$ where $a$ and $b$ are real numbers. Which of the following options is/are correct ?
Select ALL correct options:
A
$a+b=3$
B
$\operatorname{det}\left(\operatorname{adjM}^2\right)=81$
C
$(\operatorname{adj} \mathrm{M})^{-1}+\operatorname{adjM}^{-1}=-\mathrm{M}$
D
If $\mathrm{M}\left[\begin{array}{l}\alpha \\ \beta \\ \gamma\end{array}\right]=\left[\begin{array}{l}1 \\ 2 \\ 3\end{array}\right]$, then $\alpha-\beta+\gamma=3$
✓ Correct! Well done.
✗ Incorrect. Try again or view the solution.
⚠ Partially correct. Some answers are missing.
Solution
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JEE Advance
Mathematics
Easy
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