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JEE Main Matrices and Determinants questions with solutions

Matrix algebra, determinants, inverse and linear systems. 19 questions from our 2016–2025 JEE Main pattern papers, from the Class 12 Mathematics syllabus. Each has the answer and a full solution.

Also practise: Matrices and Determinants for JEE Advanced

JEE Main 2025

Let A=beginbmatrix1&2\\0&1endbmatrix and P=A+A^2+…+A^10. The sum of all entries of P isJEE Main 2025 · medium
Let a,b,c be the roots of x^3-6x^2+11x-4=0. The value of the determinant beginvmatrix1+a&1&1\\1&1+b&1\\1&1&1+cendvmatrix isJEE Main 2025 · medium
Let A=beginbmatrix1&2&2\\2&1&-2\a&2&bendbmatrix with real a,b satisfy AA^T=9I. If det A>0, the value of det A isJEE Main 2025 · hard

JEE Main 2024

A 2×2 real matrix A has trace 5 and determinant 6. Then det (A^2+I) equalsJEE Main 2024 · medium
A 3×3 real matrix A has characteristic polynomial λ^3-6λ^2+11λ-6. The value of |adj(A)+2I| isJEE Main 2024 · hard

JEE Main 2023

Let A be a 3×3 real matrix with A^2=A and tr(A)=2. Then det (I+A) equalsJEE Main 2023 · medium
If the system x+y+z=1, x+2y+4z=k, x+4y+10z=k^2 has infinitely many solutions, then the sum of all possible values of k isJEE Main 2023 · medium

JEE Main 2022

The sum of all nine entries of A^10 isJEE Main 2022 · medium
The number of matrices beginbmatrixa&b\c&dendbmatrix whose entries a,b,c,d all belong to \0,1,2\ and whose determinant is 0 isJEE Main 2022 · hard

JEE Main 2021

The sum of all the entries of A^25 isJEE Main 2021 · easy
If a,b,c are the roots of t^3-6t^2+11t-6=0, then beginvmatrixa&b&c\b&c&a\c&a&bendvmatrix equalsJEE Main 2021 · medium

JEE Main 2020

The homogeneous system x+y+z=0, 3x+ky+kz=0, -3x+y+kz=0 has a non-trivial solution for exactly two real values of k. The sum of the squares of these…JEE Main 2020 · medium

JEE Main 2019

For the matrix A=beginbmatrix1&2\\0&1endbmatrix, the total of all four entries of A^10 isJEE Main 2019 · hard
If a,b,c are the roots of x^3-5x^2+2x-1=0, then the value of beginvmatrixa&b&c\b&c&a\c&a&bendvmatrix isJEE Main 2019 · hard
For real constants λ,μ, the linear system x+y+z=6, x+2y+3z=10, x+2y+λ z=μ has infinitely many solutions. The value of λ+μ isJEE Main 2019 · hard

JEE Main 2018

For the system x+y+z=6, x+2y+3z=14, x+2y+λ z=μ to have infinitely many solutions, λ+μ must equalJEE Main 2018 · hard

JEE Main 2017

If A=beginbmatrix1&2\\3&4endbmatrix, then det (A^3 equalsJEE Main 2017 · easy
The value of the determinant beginvmatrix1&1&1\\1&2&4\\1&3&9endvmatrix isJEE Main 2017 · medium

JEE Main 2016

Let A=beginbmatrix1&1\\0&1endbmatrix and B=A+A^2+A^3+…+A^20. The sum of all four entries of B isJEE Main 2016 · medium

Other Mathematics topics

Area Under Curves 7 Binomial Theorem 12 Complex Numbers 10 Conic Sections 5 Differential Equations 9 Differentiation and Application of Derivatives 19 Indefinite and Definite Integrals 16 Limits 9 Permutations and Combinations 10 Probability 9 Quadratic Equations 9 Sequences and Series 9 Sets, Relations and Functions 10 Statistics 6 Straight Lines and Circles 9 Three Dimensional Geometry 14 Trigonometry and Inverse Trigonometric Functions 9 Vector Algebra 8