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Saturday, 31 October

JEE Main · Maths · Determinants

Trap involving |adj(A)| vs |A^-1|

JEE Main asked Trap involving |adj(A)| vs |A^-1| 10 times in 10 of the 108 shifts Lumi analysed, in 2021, 2022, 2023, 2024, 2025 and 2026. It belongs to Matrix Inverse, in Determinants (Maths). The longest wait between two years asking it was 1 year. In 2022, 2023 and 2025 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
10
in 10 shifts
Years
6 of 8
First asked
2021
last in 2026
Pattern
Asked most years
across the analysed shifts

Questions on this idea a shift, by year

2017–2026. Asked in 2021, 2022, 2023, 2024, 2025 and 2026. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.150.30’170’200.03’210.11’220.14’230.05’240.25’250.11’26

Raw count: 2017: 0 in 1 shift · 2020: 0 in 12 shifts · 2021: 1 in 24 shifts · 2022: 3 in 24 shifts · 2023: 2 in 12 shifts · 2024: 1 in 18 shifts · 2025: 2 in 8 shifts · 2026: 1 in 9 shifts.

Shift by shift

Each square is one analysed shift, in date order. Open a filled one for that paper.

  • 20261 of 9
  • 20252 of 8
  • 20241 of 18
  • 20232 of 12
  • 20223 of 24
  • 20211 of 24
  • 20200 of 12
  • 20170 of 1

Asked in that shift More than once Not asked

How JEE Main framed it

Single correct is the usual form. Skill tested: calculation.

  • Evaluate nested adjoint and inverse of matrix
  • Determinant of adjoint of matrix expression

Difficulty

Easy 0Medium 7Hard 3

1 of the 10 questions had a numerical answer.

Every question

All 10 questions

From the official JEE Main shift papers, newest first. Open one for the full question, the options and the official answer.

  1. 5 Apr 2026, Shift 1 · Q3Let A be a 3×33 \times 3 matrix such that AT[101]=[522]A^T\begin{bmatrix}1\\0\\1\end{bmatrix}=\begin{bmatrix}5\\2\\2\end{bmatrix},…HardSingle correct
  2. 3 Apr 2025, Shift 1 · Q5Let AA be a matrix of order 3×33 \times 3 and ∣A∣=5|A| = 5. If ∣2 adj(3A adj(2A))∣=2α⋅3β⋅5γ|2\,adj(3A\,adj(2A))| = 2^{\alpha}\cdot 3^{\beta}\cdot 5^{\gamma},…MediumSingle correct
  3. 2 Apr 2025, Shift 1 · Q15Let a∈Ra\in\mathbf{R} and A be a matrix of order 3×33\times3 such that det⁡(A)=−4\det(A)=-4 and…MediumSingle correct
  4. 4 Apr 2024, Shift 1 · Q5Let α∈(0,∞)\alpha \in (0, \infty) and A=[12α101012]A=\begin{bmatrix}1&2&\alpha\\1&0&1\\0&1&2\end{bmatrix}. If…HardSingle correct
  5. 13 Apr 2023, Shift 2 · Q5Let for A=[123α31112]A=\begin{bmatrix}1&2&3\\ \alpha&3&1\\ 1&1&2\end{bmatrix}, ∣A∣=2|A|=2. If ∣2 adj(2 adj(2A))∣=32n|2\,\mathrm{adj}(2\,\mathrm{adj}(2A))|=32^n, then…MediumSingle correct
  6. 10 Apr 2023, Shift 1 · Q4If AA is a 3×33\times3 matrix and ∣A∣=2|A|=2, then ∣3 adj(∣3A∣A2)∣\left|3\,adj\left(|3A|A^2\right)\right| is equal toMediumSingle correct
  7. 26 Jun 2022, Shift 1 · Q3Let A be a 3×33 \times 3 invertible matrix. If ∣adj (24A)∣=∣adj (3 adj (2A))∣|\mathrm{adj}\,(24A)| = |\mathrm{adj}\,(3\,\mathrm{adj}\,(2A))|, then ∣A∣2|A|^2 is equal to :MediumSingle correct
  8. 24 Jun 2022, Shift 1 · Q9Let S={n:1≤n≤50S = \{\sqrt{n} : 1 \le n \le 50 and n is odd}\}. Let a∈Sa \in S and…MediumSingle correct
  9. 28 Jul 2022, Shift 1 · Q14Let the matrix A=[010001100]A=\begin{bmatrix}0&1&0\\0&0&1\\1&0&0\end{bmatrix} and the matrix B0=A49+2A98B_0=A^{49}+2A^{98}. If Bn=Adj(Bn−1)B_n=\mathrm{Adj}(B_{n-1}) for…HardSingle correct
  10. 26 Aug 2021, Shift 2 · Q82Let A be a 3×33\times3 real matrix. If det⁡(2 Adj(2 Adj(Adj (2A))))=241\det(2\,\mathrm{Adj}(2\,\mathrm{Adj}(\mathrm{Adj}\,(2\mathrm{A}))))=2^{41}, then the value of…MediumNumerical value

Shifts: 26 Aug 2021, Shift 2, 24 Jun 2022, Shift 1, 26 Jun 2022, Shift 1, 28 Jul 2022, Shift 1, 10 Apr 2023, Shift 1, 13 Apr 2023, Shift 2, 4 Apr 2024, Shift 1, 2 Apr 2025, Shift 1, 3 Apr 2025, Shift 1, 5 Apr 2026, Shift 1.

Same topic

Other ideas in Matrix Inverse

Matrix Inverse has 14 ideas JEE Main has asked; 7 of them came up in more than one question. The 12 most asked are below.

Topic analysisChapter analysisStudy this chapterAll repeated ideas