Learn

Saturday, 31 October

JEE Main · Maths · Matrices

Cayley-Hamilton Theorem Application

JEE Main asked Cayley-Hamilton Theorem Application 10 times in 10 of the 108 shifts Lumi analysed, in 2021, 2022, 2024, 2025 and 2026. It belongs to Matrix Multiplication, in Matrices (Maths). The longest wait between two years asking it was 2 years. In 2021, 2022 and 2024 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
10
in 10 shifts
Years
5 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, 2024, 2025 and 2026. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.10.20’170’200.10’210.07’220’230.14’240.13’250.11’26

Raw count: 2017: 0 in 1 shift · 2020: 0 in 12 shifts · 2021: 3 in 24 shifts · 2022: 2 in 24 shifts · 2023: 0 in 12 shifts · 2024: 3 in 18 shifts · 2025: 1 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
  • 20251 of 8
  • 20243 of 18
  • 20230 of 12
  • 20222 of 24
  • 20213 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: multi-step.

  • Count correct statements on matrix identities
  • Reduce matrix power using polynomial relation

Difficulty

Easy 0Medium 7Hard 3

3 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. 2 Apr 2026, Shift 1 · Q4Let A=[121α]A=\begin{bmatrix}1&2\\1&\alpha\end{bmatrix} and B=[33β2]B=\begin{bmatrix}3&3\\\beta&2\end{bmatrix}. If A2−4A+I=OA^2-4A+I=O and B2−5B−6I=OB^2-5B-6I=O,…HardOther
  2. 2 Apr 2025, Shift 2 · Q3Let AA be a 3×33\times3 real matrix such that A2(A−2I)−4(A−I)=OA^2(A-2I) - 4(A-I) = O, where II and OO are the identity and null matrices,…MediumSingle correct
  3. 9 Apr 2024, Shift 2 · Q4Let B=[1315]B=\begin{bmatrix}1&3\\1&5\end{bmatrix} and AA be a 2×22\times2 matrix such that AB−1=A−1AB^{-1}=A^{-1}. If BCB−1=ABCB^{-1}=A and…HardSingle correct
  4. 8 Apr 2024, Shift 1 · Q4Let A=[2a013105b]A=\begin{bmatrix}2&a&0\\1&3&1\\0&5&b\end{bmatrix}. If A3=4A2−A−21IA^3=4A^2-A-21I, where II is the identity matrix of order 3×33\times3, then…MediumSingle correct
  5. 4 Apr 2024, Shift 2 · Q23Let AA be a 2×22\times2 symmetric matrix such that A[11]=[37]A\begin{bmatrix}1\\1\end{bmatrix}=\begin{bmatrix}3\\7\end{bmatrix} and the…MediumNumerical value
  6. 27 Jul 2022, Shift 2 · Q4Let A=(4−2αβ)A = \begin{pmatrix} 4 & -2 \\ \alpha & \beta \end{pmatrix}. If A2+γA+18I=OA^2 + \gamma A + 18I = O, then det (A) is equal to __________.MediumSingle correct
  7. 27 Jul 2022, Shift 1 · Q4Let A=(12−2−5)A = \begin{pmatrix} 1 & 2 \\ -2 & -5 \end{pmatrix}. Let α,β∈R\alpha, \beta \in \mathbb{R} be such that αA2+βA=2I\alpha A^2 + \beta A = 2I.…MediumSingle correct
  8. 18 Mar 2021, Shift 2 · Q82Let I be an identity matrix of order 2×22\times2 and P=[2−15−3]P=\begin{bmatrix}2&-1\\5&-3\end{bmatrix}. Then the value of n∈Nn\in\mathbb{N} for…MediumNumerical value
  9. 26 Feb 2021, Shift 2 · Q86If the matrix A=[10002030−1]A=\begin{bmatrix} 1 & 0 & 0 \\ 0 & 2 & 0 \\ 3 & 0 & -1 \end{bmatrix} satisfies the equation…HardNumerical value
  10. 27 Aug 2021, Shift 1 · Q63If the matrix A=(02K−1)A=\begin{pmatrix}0 & 2\\ K & -1\end{pmatrix} satisfies A(A3+3I)=2IA(A^3+3I)=2I, then the value of KK is :MediumSingle correct

Shifts: 26 Feb 2021, Shift 2, 18 Mar 2021, Shift 2, 27 Aug 2021, Shift 1, 27 Jul 2022, Shift 2, 27 Jul 2022, Shift 1, 4 Apr 2024, Shift 2, 8 Apr 2024, Shift 1, 9 Apr 2024, Shift 2, 2 Apr 2025, Shift 2, 2 Apr 2026, Shift 1.

Same topic

Other ideas in Matrix Multiplication

Matrix Multiplication has 19 ideas JEE Main has asked; 8 of them came up in more than one question. The 12 most asked are below.

Topic analysisChapter analysisStudy this chapterAll repeated ideas