JEE Main 2022 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 26 July 2022, Shift 1, Maths Q4

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

Let A be a

2 \times 2

matrix with

\det\,(\mathrm{A}) = -1

and

\det\,((\mathrm{A} + \mathrm{I})\,(\mathrm{Adj}\,(\mathrm{A}) + \mathrm{I})) = 4

. Then the sum of the diagonal elements of A can be :

(1) $-1$
(2) $2$ Official answer
(3) $1$
(4) $-\sqrt{2}$

Official answer

Option 2

NTA final key.

Chapter: Matrices
Topic: Matrix Inverse
Idea tested: Cofactor Matrix and Adjoint

Same idea in other shifts

Asked 6× in all

8 Apr 2026, Shift 2 · Q4Let $A = \begin{bmatrix} \alpha & 1 & 2 \\ 2 & 3 & 0 \\ 0 & 4 & 5 \end{bmatrix}$ and…HardSingle correct
5 Apr 2024, Shift 2 · Q5Let $\alpha\beta \neq 0$ and…MediumSingle correct
4 Aug 2021, Shift 1 · Q63Let $A=\begin{bmatrix}x&3&2\\1&y&4\\2&2&z\end{bmatrix}$ , $xyz=60$ and $8x+4y+3z=20$ . If $A(adj\ A)=k\,I$ , then $k$ is equal toMediumSingle correct
17 Mar 2021, Shift 1 · Q82If A $=\begin{bmatrix}2 & 3\\ 0 & -1\end{bmatrix}$ , then the value of $\det(A^{4})+\det\left(A^{10}-(\mathrm{Adj}(2A))^{10}\right)$ is…MediumNumerical value
2 Apr 2017 (offline) · Q64If $A=\begin{bmatrix}2&-3\\-4&1\end{bmatrix}$ , then $\mathrm{adj}(3A^2+12A)$ 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.