JEE Main 2026 · MathsNumerical answerNumerical valueMediumMulti-step

JEE Main 6 April 2026, Shift 1, Maths Q21

Question 21 of 75 in this shift, Maths question 21 of 25, Section B.

Let

A=\begin{bmatrix}-1&1&-1\\1&0&1\\0&0&1\end{bmatrix}

satisfy

A^2+\alpha\left(\operatorname{adj}(\operatorname{adj}(A))\right)+\beta\left(\operatorname{adj}(A)\left(\operatorname{adj}(\operatorname{adj}(A))\right)\right)=\begin{bmatrix}2&-2&2\\-2&0&-1\\0&0&-1\end{bmatrix}

for some

\alpha,\beta\in\mathbb{R}

. Then

(\alpha-\beta)^2

is equal to ________.

Official answer

NTA final key.

Chapter: Determinants
Topic: Matrix Inverse
Idea tested: Inverse Relation to Double Adjoint

Same idea in other shifts

Asked 8× in all

4 Apr 2026, Shift 1 · Q6Let $A=\begin{bmatrix}1&1&2\\-2&0&1\\1&3&5\end{bmatrix}$ . Then the sum of all elements of the matrix…MediumSingle correct
7 Apr 2025, Shift 1 · Q5Let $A$ be a $3 \times 3$ matrix such that $|\mathrm{adj}(\mathrm{adj}(\mathrm{adj}\,A))| = 81$ . If…HardSingle correct
8 Apr 2025, Shift 2 · Q4Let $A = \begin{bmatrix} 2 & 2+p & 2+p+q \\ 4 & 6+2p & 8+3p+2q \\ 6 & 12+3p & 20+6p+3q \end{bmatrix}$ . If…MediumSingle correct
6 Apr 2024, Shift 2 · Q4If $A$ is a square matrix of order 3 such that $\det(A)=3$ and…MediumSingle correct
9 Apr 2024, Shift 1 · Q23Let A be a non-singular matrix of order 3. If $\det(3\,\mathrm{adj}(2\,\mathrm{adj}((\det A)A)))=3^{-13}\cdot2^{-10}$ and…HardNumerical value
30 Jan 2024, Shift 2 · Q3Let $R = \begin{pmatrix} x & 0 & 0 \\ 0 & y & 0 \\ 0 & 0 & z \end{pmatrix}$ be a non-zero $3\times 3$ matrix, where…HardOther
31 Jan 2024, Shift 2 · Q22Let A be a $3\times3$ matrix and $\det(A)=2$ . If…MediumNumerical value

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 42 of the 174 JEE Main shifts held from 2017 to 2026.