JEE Mathematics

Algebra of Matrices: JEE Questions & Solutions

25 previous-year JEE Mathematics questions on Algebra of Matrices, each with a worked step-by-step solution.

Intermediate

Previous-year questions

  1. 01For the matrices A = 3 -4 1 -1 and B = -29 49 -13 18, if (A¹⁵ + B) x y = 0 0, then among the following which one is true?MCQMediumJEE 2026
  2. 02Let A = 0 2 -3 -2 0 1 3 -1 0 and B be a matrix such that B(I - A) = I + A. Then the sum of the diagonal elements of B^T B is equal toNVAMediumJEE 2026
  3. 03The number of 3×2 matrices A, which can be formed using the elements of the set {-2,-1,0,1,2} such that the sum of all the diagonal…NVAMediumJEE 2026
  4. 04Let A = [a_ij] be a 3 × 3 matrix such that A 0 1 0 = 0 0 1, A 4 1 3 = 0 1 0, A 2 1 2 = 1 0 0. Then a₂₃ equals:MCQEasyJEE 2025
  5. 05Let A = [ 1/√2 -2 0 1 ] and P = [ cos θ -sin θ sin θ cos θ ], θ > 0. If B = P A P^T, C = P^T B¹⁰ P, and the sum of the diagonal elements of…MCQMediumJEE 2025
  6. 06Let S = { m ∈ ℤ: A^m² + A^m = 3I - A⁻⁶ }, where A = 2 -1 1 0 Then n(S) is equal to:NVAMediumJEE 2025
  7. 07Let A = [a_ij] be a matrix of order 3 × 3, with a_ij = (√2)^(i+j). If the sum of all the elements in the third row of A² is α + β√2, where…MCQMediumJEE 2025
  8. 08Let A = α -1 6 β, α > 0, such that det(A) = 0 and α + β = 1. If I denotes the 2 × 2 identity matrix, then the matrix (I + A)⁸ is:MCQMediumJEE 2025
  9. 09Let A be a 3 × 3 real matrix such that A²(A - 2I) - 4(A - I) = O, where I and O are the identity and null matrices, respectively. If A⁵ = α…MCQMediumJEE 2025
  10. 10Let A = cos θ 0 -sin θ 0 1 0 sin θ 0 cos θ. If for some θ ∈ (0, π), A² = A^T, then the sum of the diagonal elements of the matrix ((A + I)³…NVAMediumJEE 2025
  11. 11Let the matrix A = 1 0 0 1 0 1 0 1 0 satisfy Aⁿ = Aⁿ⁻² + A² - I for n ≥ 3. Then the sum of all the elements of A⁵⁰ is:MCQMediumJEE 2025
  12. 12Given f(x)= cos x -sin x 0 sin x cos x 0 0 0 1 Evaluate: Statement I: f(-x) is the inverse of f(x). Statement II: f(x)· f(y)=f(x+y).MCQMediumJEE 2024
  13. 13Let A be a 2 × 2 real matrix and I be the identity matrix of order 2. If the roots of the equation |A - xI| = 0 are -1 and 3, then the sum…NVAEasyJEE 2024
  14. 14Let A be a square matrix such that AA^T = I. Then 1/2A[(A + A^T)² + (A - A^T)²] is equal to:MCQMediumJEE 2024
  15. 15Let R = x 0 0 0 y 0 0 0 z be a non-zero 3 × 3 matrix, where xsinθ = ysin(θ + 2π/3) = zsin(θ + 4π/3) ≠ 0, θ ∈ (0, 2π). For a square matrix…MCQMediumJEE 2024
  16. 16Let α and β be real numbers. Consider a 3 × 3 matrix A such that: A² = 3A + α I, A⁴ = 21A + β I. Then:MCQMediumJEE 2023
  17. 17Let A be a symmetric matrix such that |A| = 2 and 2 1 3 3/2 A = 1 2 α β. If the sum of the diagonal elements of A is s, then (β s)/α² is…NVAMediumJEE 2023
  18. 18Let A = 1 0 0 0 4 -1 0 12 -3 Then the sum of the diagonal elements of the matrix (A + I)¹¹ is equal to:MCQMediumJEE 2023
  19. 19If A = 1/2 1 √3 -√3 1, then:MCQMediumJEE 2023
  20. 20Let A = [a_ij]_(2× 2), where a_ij ≠ 0 for all i, j, and A² = I. Let a be the sum of all diagonal elements of A and b = |A|. Then 3a² + 4b²…MCQMediumJEE 2023
  21. 21Let P be a square matrix such that P² = I - P. For α, β, γ, δ ∈ ℕ, if P^α + P^β = γ I - 29P and P^α - P^β = δ I - 13P then α + β + γ - δ is…MCQMediumJEE 2023
  22. 22Let P = √3/2 1/2 -1/2 √3/2, A = 1 1 0 1, and Q = PAP^T. If P^TQ²⁰⁰⁷P = a b c d, then 2a + b - 3c - 4d equals:MCQMediumJEE 2023
  23. 23Let A be a 2 × 2 matrix with real entries such that A^T = α A + I, where α ∈ ℝ \ {-1, 1}. If det(A² - A) = 4, then the sum of all possible…MCQMediumJEE 2023
  24. 24Let A = 0 1 2 a 0 3 1 c 0, where a, c ∈ ℝ. If A³ = A and the positive value of a belongs to the interval (n-1, n], where n ∈ ℕ, then n is…MCQMediumJEE 2023
  25. 25Let A = 1 1/51 0 1. If B = 1 2 -1 -1 A -1 -2 1 1, then the sum of all the elements of the matrix Σ_(n=1)⁵⁰ Bⁿ is equal to:MCQMediumJEE 2023

Frequently asked questions

Our bank has 25 previous-year JEE Mathematics questions tagged to Algebra of Matrices, drawn from JEE papers between 2023 and 2026, including 3 from 2026 alone. Each comes with a full step-by-step solution.

Algebra of Matrices is rated Intermediate overall for JEE Mathematics. The PYQs on this page break down as 23 medium, 2 easy.

Of the 25 previous-year questions on Algebra of Matrices, 19 are multiple-choice (MCQ) and 6 are numerical-value (NVA) questions.

Based on recent paper analysis, Algebra of Matrices is worth about 2 marks in JEE Main. It sits in Matrices & Determinants, a Class 12 Mathematics chapter.

More Matrices & Determinants topics

Solving Linear Equations (Matrix Method)40Inverse & Adjoint of a Matrix22Determinants Basics16Properties of Determinants11Types of Matrices3

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