JEE Main 2023 · MathsMultiple choiceSingle correctMediumCalculation

JEE Main 10 April 2023, Shift 1, Maths Q4

Question 4 of 90 in this shift, Maths question 4 of 30, Section A.

A

is a

3\times3

matrix and

|A|=2

, then

\left|3\,adj\left(|3A|A^2\right)\right|

is equal to

(1) $3^{12}\cdot6^{11}$
(2) $3^{12}\cdot6^{10}$
(3) $3^{10}\cdot6^{11}$
(4) $3^{11}\cdot6^{10}$ Official answer

Official answer

Option 4

NTA final key.

Chapter: Determinants
Topic: Matrix Inverse
Idea tested: Trap involving |adj(A)| vs |A^-1|

Same idea in other shifts

Asked 10× in all

5 Apr 2026, Shift 1 · Q3Let A be a $3 \times 3$ matrix such that $A^T\begin{bmatrix}1\\0\\1\end{bmatrix}=\begin{bmatrix}5\\2\\2\end{bmatrix}$ ,…HardSingle correct
2 Apr 2025, Shift 1 · Q15Let $a\in\mathbf{R}$ and A be a matrix of order $3\times3$ such that $\det(A)=-4$ and…MediumSingle correct
3 Apr 2025, Shift 1 · Q5Let $A$ be a matrix of order $3 \times 3$ and $|A| = 5$ . If $|2\,adj(3A\,adj(2A))| = 2^{\alpha}\cdot 3^{\beta}\cdot 5^{\gamma}$ ,…MediumSingle correct
4 Apr 2024, Shift 1 · Q5Let $\alpha \in (0, \infty)$ and $A=\begin{bmatrix}1&2&\alpha\\1&0&1\\0&1&2\end{bmatrix}$ . If…HardSingle correct
13 Apr 2023, Shift 2 · Q5Let for $A=\begin{bmatrix}1&2&3\\ \alpha&3&1\\ 1&1&2\end{bmatrix}$ , $|A|=2$ . If $|2\,\mathrm{adj}(2\,\mathrm{adj}(2A))|=32^n$ , then…MediumSingle correct
28 Jul 2022, Shift 1 · Q14Let the matrix $A=\begin{bmatrix}0&1&0\\0&0&1\\1&0&0\end{bmatrix}$ and the matrix $B_0=A^{49}+2A^{98}$ . If $B_n=\mathrm{Adj}(B_{n-1})$ for…HardSingle correct
24 Jun 2022, Shift 1 · Q9Let $S = \{\sqrt{n} : 1 \le n \le 50$ and n is odd $\}$ . Let $a \in S$ and…MediumSingle correct
26 Jun 2022, Shift 1 · Q3Let A be a $3 \times 3$ invertible matrix. If $|\mathrm{adj}\,(24A)| = |\mathrm{adj}\,(3\,\mathrm{adj}\,(2A))|$ , then $|A|^2$ is equal to :MediumSingle correct

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.