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Saturday, 31 October

JEE Main · Maths · Matrices

Idempotent and Nilpotent Matrices

JEE Main asked Idempotent and Nilpotent Matrices 2 times in 2 of the 108 shifts Lumi analysed, in 2022 and 2025. It belongs to Matrix Multiplication, in Matrices (Maths). The longest wait between two years asking it was 3 years.

Updated 2026-10-24

Times asked
2
in 2 shifts
Years
2 of 8
First asked
2022
last in 2025
Pattern
Occasional
across the analysed shifts

Questions on this idea a shift, by year

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

00.10.20’170’200’210.04’220’230’240.13’250’26

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

Shift by shift

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

  • 20260 of 9
  • 20251 of 8
  • 20240 of 18
  • 20230 of 12
  • 20221 of 24
  • 20210 of 24
  • 20200 of 12
  • 20170 of 1

Asked in that shift More than once Not asked

How JEE Main framed it

Numerical value is the usual form. Skill tested: multi-step.

  • Power of matrix via idempotent property
  • Matrix powers satisfying matrix equation

Difficulty

Easy 0Medium 2Hard 0

1 of the 2 questions had a numerical answer.

Every question

All 2 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 2025, Shift 1 · Q18Let A=[α−16β]A=\begin{bmatrix}\alpha&-1\\6&\beta\end{bmatrix}, α>0\alpha>0, such that det⁡(A)=0\det(A)=0 and α+β=1\alpha+\beta=1. If I denotes 2×22\times2…MediumSingle correct
  2. 25 Jun 2022, Shift 2 · Q21Let A=(2−21−1)A = \begin{pmatrix} 2 & -2 \\ 1 & -1 \end{pmatrix} and B=(−12−12)B = \begin{pmatrix} -1 & 2 \\ -1 & 2 \end{pmatrix}. Then the number of…MediumNumerical value

Shifts: 25 Jun 2022, Shift 2, 2 Apr 2025, 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