JEE Main · Maths · Determinants

Matrix Inverse: JEE Main previous year questions

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

51 questions in the 108 JEE Main shifts Lumi analysed, in 8 of 8 years. Pattern: Asked most years. 21 came in 2024–26. Here is how it is asked and which ideas come back.

Questions: 51; in 50 of 108 shifts
Years asked: 8/8; last asked 2026
Chance in a shift: 47%; calibrated model, how we compute it
Weighted estimate: 0.6; model; history: 0.5 a shift on average, typically 0.3–0.8

Key findings

01
Asked in 8 of 8 years with analysed shifts and in 50 of 108 shifts: 51 questions, #56 of 196 topics. It came in every year with analysed shifts.
02
30% of its questions since 2020 tested an idea no earlier year had asked; 25 repeated an idea from the year before.
03
The most repeated idea is Inverse Relation to Double Adjoint, asked 16 times in 16 shifts (2020, 2022, 2023, 2024, 2025, 2026), most often as “evaluate nested adjoint and inverse of matrix”.
04
JEE Main has asked 14 of the 52 ideas in this topic; 31 have never been asked, directly or inside another question.
05
Mostly asked as single correct (71%); 25% need a numerical answer, 6% are easy and 27% hard.
06
The skill tested most is multi-step (67%), then calculation (29%).

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: 1 in 1 shift · 2020: 3 in 12 shifts · 2021: 8 in 24 shifts · 2022: 11 in 24 shifts · 2023: 7 in 12 shifts · 2024: 8 in 18 shifts · 2025: 6 in 8 shifts · 2026: 7 in 9 shifts.

Up to 2023: 0.5; a shift, of 25
Since 2024: 0.6; 0.2
Usual gap: 1.3 yrs; between years asking it
Shifts with it: 50/108; 46% of analysed shifts

Recent framings

determinant involving adjoint matrix
numerical: matrix identity with adjoints
singular matrix parameter then extrema of integral

Revise first

Inverse Relation to Double Adjoint · asked 2020, 2022, 2023, 2024, 2025, 2026
Trap involving |adj(A)| vs |A^-1| · asked 2021, 2022, 2023, 2024, 2025, 2026
Cofactor Matrix and Adjoint · asked 2017, 2021, 2022, 2024, 2026

How it is asked

Difficulty, format and skill

Across all 51 questions on Matrix Inverse since 2017.

Difficulty

QUESTIONS

3414

Easy3 · 6%
Medium34 · 67%
Hard14 · 27%

Format

Single correct · 36 Q71%
Numerical value · 13 Q25%
Other · 1 Q2%
Two statements · 1 Q2%

Skill tested

Multi-step · 34 Q67%
Calculation · 15 Q29%
Conceptual · 2 Q4%

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 14 of the 52 ideas in this topic. 31 have never been asked yet.

14731

Asked directly14 · 27%
Touched inside another question7 · 13%
Never asked31 · 60%

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

Open37 · 73%73%8/82576745
6 ideas inside
- OpenRepeated15 · 41%41%6/822442
- OpenRepeated10 · 27%27%6/8322
- OpenRepeated5 · 14%14%4/82
- OpenRepeated5 · 14%14%3/822
- Open1 · 3%3%1/8
- Open1 · 3%3%1/8
Open14 · 27%27%7/83422

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

14 different ideas were tested; 7 came more than once.

Inverse Relation to Double Adjoint16×
evaluate nested adjoint and inverse of matrix
Single correct · 16 shifts · 5 numerical
Trap involving |adj(A)| vs |A^-1|10×
evaluate nested adjoint and inverse of matrix
Single correct · 10 shifts · 1 numerical
Cofactor Matrix and Adjoint6×
evaluate nested adjoint and inverse of matrix
Single correct · 6 shifts · 1 numerical
Determinant of Adjoint of Inverse5×
evaluate nested adjoint and inverse of matrix
Single correct · 5 shifts
Solving Matrix Equations3×
solve matrix equation pa=b
Single correct · 3 shifts · 1 numerical
Singular and Non-singular Matrices2×
singular matrix parameter then extrema of integral
Numerical value · 2 shifts · 1 numerical
Inverse via Characteristic Equation2×
matrix inverse as linear combination via characteristic equation
Single correct · 2 shifts
Commutativity of Adjoint and Inverse1×
determinant of adjoint and inverse expression
Numerical value · 1 shift · 1 numerical
Inverse of Orthogonal Matrices1×
statement i/ii on matrix
Two statements · 1 shift
Elementary Row Transformations1×
identify matrix not obtainable by elementary row operation
Single correct · 1 shift
Inverse of Involutory Matrices1×
count matrices with a equal to inverse
Numerical value · 1 shift · 1 numerical
Inverse of Skew-Symmetric Matrices1×
entries of matrix expression
Numerical value · 1 shift · 1 numerical
Inverse via Adjoint Formula1×
unknown parameters from matrix inverse relation
Numerical value · 1 shift · 1 numerical
Properties of Matrix Inverses1×
evaluate nested adjoint and inverse of matrix
Single correct · 1 shift

Idea	Times	Shifts	Format	Numerical
Inverse Relation to Double Adjointevaluate nested adjoint and inverse of matrix	16	16	Single correctMulti-step	5
Trap involving \|adj(A)\| vs \|A^-1\|evaluate nested adjoint and inverse of matrix	10	10	Single correctCalculation	1
Cofactor Matrix and Adjointevaluate nested adjoint and inverse of matrix	6	6	Single correctMulti-step	1
Determinant of Adjoint of Inverseevaluate nested adjoint and inverse of matrix	5	5	Single correctMulti-step	–
Solving Matrix Equationssolve matrix equation pa=b	3	3	Single correctMulti-step	1
Singular and Non-singular Matricessingular matrix parameter then extrema of integral	2	2	Numerical valueMulti-step	1
Inverse via Characteristic Equationmatrix inverse as linear combination via characteristic equation	2	2	Single correctCalculation	–
Commutativity of Adjoint and Inversedeterminant of adjoint and inverse expression	1	1	Numerical valueMulti-step	1
Inverse of Orthogonal Matricesstatement i/ii on matrix	1	1	Two statementsConceptual	–
Elementary Row Transformationsidentify matrix not obtainable by elementary row operation	1	1	Single correctConceptual	–
Inverse of Involutory Matricescount matrices with a equal to inverse	1	1	Numerical valueMulti-step	1
Inverse of Skew-Symmetric Matricesentries of matrix expression	1	1	Numerical valueMulti-step	1
Inverse via Adjoint Formulaunknown parameters from matrix inverse relation	1	1	Numerical valueMulti-step	1
Properties of Matrix Inversesevaluate nested adjoint and inverse of matrix	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 Inverse 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 Inverse questions, year by year

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JEE Main 20248 questions in 8 shifts

JEE Main 20237 questions in 7 shifts

JEE Main 202211 questions in 11 shifts

JEE Main 20218 questions in 8 shifts

JEE Main 20203 questions in 3 shifts

JEE Main 20171 question in 1 shift

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