JEE Main Math · U3
Matrices and Determinants
JEE Main level practice on matrix algebra, determinants, adjoint, inverse, triangle area, and consistency of linear systems.
Test yourself
A focused, distraction-free run through 50 multiple-choice questions. Hints if you need them; your score at the end.
Difficulty guide
The label describes the problem, not your ability.
1/5 - Foundational
Warm-up setup; checks one basic idea.
2/5 - Routine exam skill
Normal syllabus skill; usually one main rule or interpretation.
3/5 - Standard multi-step
Exam-style problem with multiple steps or a common trap.
4/5 - Hard exam skill
High-end exam problem; combines methods carefully.
5/5 - Challenge
Stretch problem beyond normal exam pressure.
Topic 3.1
Matrix Algebra, Types, and Powers
Products, transpose structure, trace-det identities, special matrices, and powers.
Item 1
Open
Item 2
Open
Item 3
Open
Item 4
Open
Item 5
Open
Item 6
Open
Item 7
Open
Item 8
Open
Item 9
Open
Item 10
Open
Item 11
Open
Item 12
Open
Item 13
Open
Item 14
Open
Item 15
Open
Topic 3.2
Determinant Properties and Evaluation
Order two and three determinants, row-column operations, adjoint determinant identities, and parameter tests.
Item 1
Open
Item 2
Open
Item 3
Open
Item 4
Open
Item 5
Open
Item 6
Open
Item 7
Open
Item 8
Open
Item 9
Open
Item 10
Open
Item 11
Open
Item 12
Open
Item 13
Open
Item 14
Open
Item 15
Open
Topic 3.3
Adjoint, Inverse, and Matrix Equations
Inverse computation, adjoint identities, invertibility parameters, and algebraic matrix equations.
Item 1
Open
Item 2
Open
Item 3
Open
Item 4
Open
Item 5
Open
Item 6
Open
Item 7
Open
Item 8
Open
Item 9
Open
Item 10
Open
Item 11
Open
Item 12
Open
Item 13
Open
Item 14
Open
Item 15
Open
Topic 3.4
Consistency and Linear Systems
Unique solution, no solution, infinitely many solutions, homogeneous systems, and Cramer's-rule style reasoning.
Item 1
Open
Item 2
Open
Item 3
Open
Item 4
Open
Item 5
Open
Item 6
Open
Item 7
Open
Item 8
Open
Item 9
Open
Item 10
Open
Item 11
Open
Item 12
Open
Item 13
Open
Item 14
Open
Item 15
Open
Topic 3.5
Determinant Applications and Mixed Parameters
Triangle area, collinearity, transformation area scale, and mixed matrix-determinant parameter reasoning.
Item 1
Open
Item 2
Open
Item 3
Open
Item 4
Open
Item 5
Open
Item 6
Open
Item 7
Open
Item 8
Open
Item 9
Open
Item 10
Open
Item 11
Open
Item 12
Open
Item 13
Open
Item 14
Open
Item 15
Open