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Saturday, 31 October

JEE Main · Maths · Determinants

Inverse Relation to Double Adjoint

JEE Main asked Inverse Relation to Double Adjoint 16 times in 16 of the 108 shifts Lumi analysed, in 2020, 2022, 2023, 2024, 2025 and 2026. It belongs to Matrix Inverse, in Determinants (Maths). The longest wait between two years asking it was 2 years. In 2020, 2022, 2023, 2024, 2025 and 2026 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
16
in 16 shifts
Years
6 of 8
First asked
2020
last in 2026
Pattern
Asked most years
across the analysed shifts

Questions on this idea a shift, by year

2017–2026. Asked in 2020, 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.

00.150.30’170.17’200’210.07’220.28’230.19’240.25’250.22’26

Raw count: 2017: 0 in 1 shift · 2020: 2 in 12 shifts · 2021: 0 in 24 shifts · 2022: 2 in 24 shifts · 2023: 4 in 12 shifts · 2024: 4 in 18 shifts · 2025: 2 in 8 shifts · 2026: 2 in 9 shifts.

Shift by shift

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

  • 20262 of 9
  • 20252 of 8
  • 20244 of 18
  • 20234 of 12
  • 20222 of 24
  • 20210 of 24
  • 20202 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: multi-step.

  • Evaluate nested adjoint and inverse of matrix
  • Matrix identity with adjoints

Difficulty

Easy 0Medium 11Hard 5

5 of the 16 questions had a numerical answer.

Every question

All 16 questions

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

  1. 6 Apr 2026, Shift 1 · Q21Let A=[−11−1101001]A=\begin{bmatrix}-1&1&-1\\1&0&1\\0&0&1\end{bmatrix} satisfy…MediumNumerical value
  2. 4 Apr 2026, Shift 1 · Q6Let A=[112−201135]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
  3. 8 Apr 2025, Shift 2 · Q4Let A=[22+p2+p+q46+2p8+3p+2q612+3p20+6p+3q]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
  4. 7 Apr 2025, Shift 1 · Q5Let AA be a 3×33 \times 3 matrix such that ∣adj(adj(adj A))∣=81|\mathrm{adj}(\mathrm{adj}(\mathrm{adj}\,A))| = 81. If…HardSingle correct
  5. 31 Jan 2024, Shift 2 · Q22Let A be a 3×33\times3 matrix and det⁡(A)=2\det(A)=2. If…MediumNumerical value
  6. 30 Jan 2024, Shift 2 · Q3Let R=(x000y000z)R = \begin{pmatrix} x & 0 & 0 \\ 0 & y & 0 \\ 0 & 0 & z \end{pmatrix} be a non-zero 3×33\times 3 matrix, where…HardOther
  7. 9 Apr 2024, Shift 1 · Q23Let A be a non-singular matrix of order 3. If det⁡(3 adj(2 adj((det⁡A)A)))=3−13⋅2−10\det(3\,\mathrm{adj}(2\,\mathrm{adj}((\det A)A)))=3^{-13}\cdot2^{-10} and…HardNumerical value
  8. 6 Apr 2024, Shift 2 · Q4If AA is a square matrix of order 3 such that det⁡(A)=3\det(A)=3 and…MediumSingle correct
  9. 15 Apr 2023, Shift 1 · Q4Let the determinant of a square matrix A of order mm be m−nm-n, where mm and nn satisfy 4m+n=224m+n=22 and 17m+4n=9317m+4n=93. If…MediumSingle correct
  10. 13 Apr 2023, Shift 1 · Q3Let B=[13α123αα4]B=\begin{bmatrix}1&3&\alpha\\1&2&3\\\alpha&\alpha&4\end{bmatrix}, α>2\alpha>2 be the adjoint of a matrix AA and ∣A∣=2|A|=2. Then…HardSingle correct
  11. 10 Apr 2023, Shift 2 · Q4If A=15! 6! 7![5!6!7!6!7!8!7!8!9!]A = \frac{1}{5!\,6!\,7!}\begin{bmatrix} 5! & 6! & 7! \\ 6! & 7! & 8! \\ 7! & 8! & 9! \end{bmatrix}, then…MediumSingle correct
  12. 8 Apr 2023, Shift 1 · Q4Let A=[21012−10−12]A=\begin{bmatrix}2&1&0\\1&2&-1\\0&-1&2\end{bmatrix}. If ∣adj(adj(adj 2A))∣=(16)n|adj(adj(adj\,2A))|=(16)^n, then nn is equal toMediumSingle correct
  13. 27 Jun 2022, Shift 1 · Q23The positive value of the determinant of the matrix A, whose…MediumNumerical value
  14. 27 Jul 2022, Shift 2 · Q21Consider a matrix…HardNumerical value
  15. 3 Sep 2020, Shift 2 · Q54Let A be a 3×33 \times 3 matrix such that adj A=[2−11−1021−2−1]\mathrm{adj}\, A = \begin{bmatrix} 2 & -1 & 1 \\ -1 & 0 & 2 \\ 1 & -2 & -1 \end{bmatrix} and…MediumSingle correct
  16. 9 Jan 2020, Shift 1 · Q54If the matrices A=[1121341−13]\mathrm{A}=\begin{bmatrix}1&1&2\\1&3&4\\1&-1&3\end{bmatrix}, B=adj A\mathrm{B}=\mathrm{adj}\,\mathrm{A} and…MediumSingle correct

Shifts: 9 Jan 2020, Shift 1, 3 Sep 2020, Shift 2, 27 Jun 2022, Shift 1, 27 Jul 2022, Shift 2, 8 Apr 2023, Shift 1, 10 Apr 2023, Shift 2, 13 Apr 2023, Shift 1, 15 Apr 2023, Shift 1, 30 Jan 2024, Shift 2, 31 Jan 2024, Shift 2, 6 Apr 2024, Shift 2, 9 Apr 2024, Shift 1, 7 Apr 2025, Shift 1, 8 Apr 2025, Shift 2, 4 Apr 2026, Shift 1, 6 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