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Saturday, 31 October

JEE Main · Maths · Matrices

Inverse via Characteristic Equation

JEE Main asked Inverse via Characteristic Equation 2 times in 2 of the 108 shifts Lumi analysed, in 2020 and 2023. It belongs to Matrix Inverse, 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
2020
last in 2023
Pattern
Occasional
across the analysed shifts

Questions on this idea a shift, by year

2017–2026. Asked in 2020 and 2023. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.050.10’170.08’200’210’220.07’230’240’250’26

Raw count: 2017: 0 in 1 shift · 2020: 1 in 12 shifts · 2021: 0 in 24 shifts · 2022: 0 in 24 shifts · 2023: 1 in 12 shifts · 2024: 0 in 18 shifts · 2025: 0 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
  • 20250 of 8
  • 20240 of 18
  • 20231 of 12
  • 20220 of 24
  • 20210 of 24
  • 20201 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.

  • Matrix inverse as linear combination via characteristic equation
  • Express inverse of 2x2 matrix via characteristic equation

Difficulty

Easy 1Medium 1Hard 0

Every question was multiple choice.

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. 8 Apr 2023, Shift 2 · Q4If A=[15λ10]A = \begin{bmatrix} 1 & 5 \\ \lambda & 10 \end{bmatrix}, A−1=αA+βIA^{-1} = \alpha A + \beta I and α+β=−2\alpha + \beta = -2, then…MediumSingle correct
  2. 8 Jan 2020, Shift 2 · Q54If A=(2294)A = \begin{pmatrix} 2 & 2 \\ 9 & 4 \end{pmatrix} and I=(1001)I = \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}, then 10A−110A^{-1} is equal to :EasySingle correct

Shifts: 8 Jan 2020, Shift 2, 8 Apr 2023, Shift 2.

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