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Saturday, 31 October

JEE Main · Maths · Matrices

Orthogonal Matrix Multiplication Definition

JEE Main asked Orthogonal Matrix Multiplication Definition 2 times in 2 of the 108 shifts Lumi analysed, in 2021 and 2024. 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
2021
last in 2024
Pattern
Occasional
across the analysed shifts

Questions on this idea a shift, by year

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

00.050.10’170’200.03’210’220’230.05’240’250’26

Raw count: 2017: 0 in 1 shift · 2020: 0 in 12 shifts · 2021: 1 in 24 shifts · 2022: 0 in 24 shifts · 2023: 0 in 12 shifts · 2024: 1 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
  • 20241 of 18
  • 20230 of 12
  • 20220 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: application.

  • Simplify matrix expression using orthogonality
  • Unknown entries from orthogonal matrix condition

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. 29 Jan 2024, Shift 1 · Q4Let A be a square matrix such that AAT=IAA^T=I. Then 12A[(A+AT)2+(A−AT)2]\frac{1}{2}A\left[(A+A^T)^2+(A-A^T)^2\right] is equal toMediumSingle correct
  2. 25 Feb 2021, Shift 2 · Q61If for the matrix, A=[1−ααβ]A = \begin{bmatrix} 1 & -\alpha \\ \alpha & \beta \end{bmatrix}, AAT=I2AA^T = I_2, then the value of α4+β4\alpha^4 + \beta^4…EasySingle correct

Shifts: 25 Feb 2021, Shift 2, 29 Jan 2024, 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