JEE Main · Maths · Matrices

Matrix Multiplication: JEE Main previous year questions

Name: Matrix Multiplication: JEE Main previous year questions
Creator: Lumi

60 questions in the 108 JEE Main shifts Lumi analysed, in 7 of 8 years. Pattern: Asked most years. 14 came in 2024–26. Here is how it is asked and which ideas come back.

Questions: 60; in 54 of 108 shifts
Years asked: 7/8; last asked 2026
Chance in a shift: 47%; calibrated model, how we compute it
Weighted estimate: 0.4; model; history: 0.4 a shift on average, typically 0.3–0.6

Key findings

01
Asked in 7 of 8 years with analysed shifts and in 54 of 108 shifts: 60 questions, #41 of 196 topics.
02
38% of its questions since 2020 tested an idea no earlier year had asked; 29 repeated an idea from the year before.
03
The most repeated idea is Powers of Square Matrices, asked 21 times in 21 shifts (2020, 2021, 2022, 2023, 2024, 2025), most often as “sum of elements of high matrix power from recurrence”.
04
JEE Main has asked 19 of the 52 ideas in this topic; 27 have never been asked, directly or inside another question.
05
Mostly asked as single correct (58%); 40% need a numerical answer, 10% are easy and 25% hard.
06
The skill tested most is multi-step (65%), then calculation (20%).

Questions a shift, year by year

Out of the 25 Maths questions in a shift. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift.

Raw count: 2017: 0 in 1 shift · 2020: 5 in 12 shifts · 2021: 17 in 24 shifts · 2022: 18 in 24 shifts · 2023: 6 in 12 shifts · 2024: 8 in 18 shifts · 2025: 3 in 8 shifts · 2026: 3 in 9 shifts.

Up to 2023: 0.4; a shift, of 25
Since 2024: 0.4; 0.0
Usual gap: 1.0 yrs; between years asking it
Shifts with it: 54/108; 50% of analysed shifts

How it is asked

Difficulty, format and skill

Across all 60 questions on Matrix Multiplication since 2017.

Difficulty

QUESTIONS

63915

Easy6 · 10%
Medium39 · 65%
Hard15 · 25%

Format

Single correct · 35 Q58%
Numerical value · 24 Q40%
Other · 1 Q2%

Skill tested

Multi-step · 39 Q65%
Calculation · 12 Q20%
Application · 7 Q12%
Conceptual · 2 Q3%

Repeats

New idea, or one asked before?

Each column is a year. Blue questions tested an idea no earlier year had asked; navy ones went back to an idea from an earlier year. 2017 is the first year, so everything in it counts as new. Heights are question counts, and Lumi analysed 1 to 24 shifts a year, so compare the split inside a column rather than heights across years.

’17’20’21’22’23’24’25’26

Idea asked for the first time
Idea asked in an earlier year

Coverage of the topic

JEE Main has asked 19 of the 52 ideas in this topic. 27 have never been asked yet.

19627

Asked directly19 · 37%
Touched inside another question6 · 12%
Never asked27 · 52%

Ideas come from Lumi’s JEE syllabus map. A never-asked idea is not a safe skip: across all of JEE Main, 22% of questions since 2024 tested an idea no earlier year had asked.

Drill down

Chapter, idea, question

Every idea JEE Main tested in this topic, with its eight years. Open one to read the questions.

chapterAskedShareYears’17’20’21’22’23’24’25’26

Open51 · 85%85%7/8415156533
18 ideas inside
- OpenRepeated20 · 39%39%6/826542
- OpenRepeated9 · 18%18%5/8322
- OpenRepeated3 · 6%6%2/82
- OpenRepeated2 · 4%4%2/8
- OpenRepeated2 · 4%4%2/8
- OpenRepeated2 · 4%4%2/8
- OpenRepeated2 · 4%4%2/8
- Open1 · 2%2%1/8
- Open1 · 2%2%1/8
- Open1 · 2%2%1/8
- Open1 · 2%2%1/8
- Open1 · 2%2%1/8
- Open1 · 2%2%1/8
- Open1 · 2%2%1/8
- Open1 · 2%2%1/8
- Open1 · 2%2%1/8
- Open1 · 2%2%1/8
- Open1 · 2%2%1/8
Open9 · 15%15%4/8233

Squares are the 8 years with analysed shifts, 2017 to 2026. A number is the questions that year when there is more than one; the shade is scaled to one shift, so a year with more analysed shifts (1 to 24 a year) does not look darker. Share is of the level above.

Ideas

Every idea inside this topic

19 different ideas were tested; 8 came more than once.

Powers of Square Matrices21×
sum of elements of high matrix power from recurrence
Single correct · 21 shifts · 10 numerical
Cayley-Hamilton Theorem Application10×
count correct statements on matrix identities
Single correct · 10 shifts · 3 numerical
Determinant of Product6×
determinant and trace of matrix from column equations
Single correct · 5 shifts · 1 numerical
Binomial Expansion for Commuting Matrices3×
entries of high matrix power
Single correct · 3 shifts · 1 numerical
Row-by-Column Multiplication3×
unknown parameter from matrix product norm condition
Numerical value · 3 shifts · 2 numerical
Idempotent and Nilpotent Matrices2×
power of matrix via idempotent property
Numerical value · 2 shifts · 1 numerical
Orthogonal Matrix Multiplication Definition2×
simplify matrix expression using orthogonality
Single correct · 2 shifts
Trace of A times A Transpose2×
count matrices with trace condition
Numerical value · 2 shifts · 1 numerical
Matrix Polynomials1×
count matrices satisfying matrix polynomial equation
Single correct · 1 shift
Involutory Matrix Properties1×
trace and determinant of involutory matrix
Single correct · 1 shift
Transpose Reversal Law1×
unknown parameter from matrix transpose relation
Single correct · 1 shift
Binomial Expansion for Non-Commuting Matrices1×
unknown parameter from matrix equation
Numerical value · 1 shift · 1 numerical
Inverse of (I+A) for Nilpotent Matrices1×
matrix polynomial in nilpotent matrix with given inverse
Numerical value · 1 shift · 1 numerical
Periodic Matrices1×
count n for which matrix power equals matrix
Numerical value · 1 shift · 1 numerical
Powers of Skew-Symmetric Matrices1×
classify matrix from sums of powers
Single correct · 1 shift
Product of Symmetric Matrices1×
identify false statement on symmetric matrices
Single correct · 1 shift
Square of Skew-Symmetric Matrix1×
find parameter from matrix power series
Numerical value · 1 shift · 1 numerical
Non-commutativity Property1×
count matrices commuting with given matrix
Numerical value · 1 shift · 1 numerical
Orthogonal Matrix Properties1×
orthogonal matrix condition on entries
Single correct · 1 shift

Idea	Times	Shifts	Format	Numerical
Powers of Square Matricessum of elements of high matrix power from recurrence	21	21	Single correctMulti-step	10
Cayley-Hamilton Theorem Applicationcount correct statements on matrix identities	10	10	Single correctMulti-step	3
Determinant of Productdeterminant and trace of matrix from column equations	6	5	Single correctCalculation	1
Binomial Expansion for Commuting Matricesentries of high matrix power	3	3	Single correctMulti-step	1
Row-by-Column Multiplicationunknown parameter from matrix product norm condition	3	3	Numerical valueCalculation	2
Idempotent and Nilpotent Matricespower of matrix via idempotent property	2	2	Numerical valueMulti-step	1
Orthogonal Matrix Multiplication Definitionsimplify matrix expression using orthogonality	2	2	Single correctApplication	–
Trace of A times A Transposecount matrices with trace condition	2	2	Numerical valueApplication	1
Matrix Polynomialscount matrices satisfying matrix polynomial equation	1	1	Single correctMulti-step	–
Involutory Matrix Propertiestrace and determinant of involutory matrix	1	1	Single correctMulti-step	–
Transpose Reversal Lawunknown parameter from matrix transpose relation	1	1	Single correctMulti-step	–
Binomial Expansion for Non-Commuting Matricesunknown parameter from matrix equation	1	1	Numerical valueCalculation	1
Inverse of (I+A) for Nilpotent Matricesmatrix polynomial in nilpotent matrix with given inverse	1	1	Numerical valueMulti-step	1
Periodic Matricescount n for which matrix power equals matrix	1	1	Numerical valueMulti-step	1
Powers of Skew-Symmetric Matricesclassify matrix from sums of powers	1	1	Single correctMulti-step	–
Product of Symmetric Matricesidentify false statement on symmetric matrices	1	1	Single correctConceptual	–
Square of Skew-Symmetric Matrixfind parameter from matrix power series	1	1	Numerical valueMulti-step	1
Non-commutativity Propertycount matrices commuting with given matrix	1	1	Numerical valueMulti-step	1
Orthogonal Matrix Propertiesorthogonal matrix condition on entries	1	1	Single correctMulti-step	–

Times and shifts count every analysed shift. Across JEE Main, 78% of questions since 2024 went back to an idea an earlier year had asked; the rest were new. All repeated ideas

Every question

Matrix Multiplication questions, year by year

The newest 40 show their opening words as they appeared in the official paper; older ones name the idea they tested. Open one for its options and the official answer.

Questions from the official JEE Main Paper 1 shifts published by NTA (CBSE for 2017). Questions NTA dropped are left out. Topic and idea tags, counts and notes are Lumi’s.

Key findings

Questions a shift, year by year

Difficulty, format and skill

Difficulty

Format

Skill tested

New idea, or one asked before?

Coverage of the topic

Chapter, idea, question

Every idea inside this topic

Matrix Multiplication questions, year by year

JEE Main 20263 questions in 3 shifts

JEE Main 20253 questions in 3 shifts

JEE Main 20248 questions in 6 shifts

JEE Main 20236 questions in 5 shifts

JEE Main 202218 questions in 16 shifts

JEE Main 202117 questions in 16 shifts

JEE Main 20205 questions in 5 shifts

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