JEE Main 2020 · MathsMultiple choiceSingle correctMediumCalculation

JEE Main 3 September 2020, Shift 2, Maths Q54

Question 54 of 75 in this shift, Maths question 4 of 25.

Let A be a

3 \times 3

matrix such that

\mathrm{adj}\, A = \begin{bmatrix} 2 & -1 & 1 \\ -1 & 0 & 2 \\ 1 & -2 & -1 \end{bmatrix}

and

B = \mathrm{adj}(\mathrm{adj}\, A)

. If

|A| = \lambda

and

|(B^{-1})^T| = \mu

, then the ordered pair,

(|\lambda|, \mu)

is equal to :

(1) $\left(9, \frac{1}{81}\right)$
(2) $\left(3, \frac{1}{81}\right)$ Official answer
(3) $(3, 81)$
(4) $\left(9, \frac{1}{9}\right)$

Official answer

Option 2

NTA final key (Sep 2020).

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

Same idea in other shifts

Asked 16× 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
6 Apr 2026, Shift 1 · Q21Let $A=\begin{bmatrix}-1&1&-1\\1&0&1\\0&0&1\end{bmatrix}$ satisfy…MediumNumerical value
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 108 of the 174 JEE Main shifts held from 2017 to 2026.