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Mathematics - Matrices

Practise 221 JEE Main previous year questions on Matrices, compiled from papers spanning 2003 to 2026. Each question is pulled directly from the actual exam paper it appeared in, so you're practising in the exact style and difficulty JEE Main tests.

Matrices has been asked in 24 of the 25 years of JEE Main papers analysed (2002–2026), with 221 questions in all. 19% of them were easy, 52% moderate and 29% tough. Most of its questions came from 2022, with 32 questions that year. In the last three years (2024–2026) it had 54 questions across 49 papers, about 1.1 per paper.

The chapter's 8 topics are not weighted equally: Product of Matrices (83 questions, 38%), Adjoint and its Properties (57 questions, 26%), and Inverse of a Matrix (26 questions, 12%) have been asked the most. Over the last five years the most frequent topics have been Adjoint and its Properties (45), Product of Matrices (41), and Formation and Basic of Matrix (15). Product of Matrices has produced the most tough questions (22).

  1. 1Let and . If , then equals:08 Apr, 2026 (E)Adjoint and its Properties
  2. 2Let satisfy for some . Then is equal to _______06 Apr, 2026 (M)Adjoint and its Properties
  3. 3Let and , . If , then the value of is :06 Apr, 2026 (E)Product of Matrices
  4. 4Let be a matrix such that , , and . If , then is equal to:05 Apr, 2026 (M)Adjoint and its Properties
  5. 5Let be a matrix such that , and . If , then equals :05 Apr, 2026 (E)Formation and Basic of Matrix
  6. 6Let be a set of matrices. Then the number of matrices in , for which the sum of the diagonal elements is equal to , is:04 Apr, 2026 (M)Product of Matrices
  7. 7Let . Then the sum of all elements of the matrix is equal to:04 Apr, 2026 (M)Adjoint and its Properties
  8. 8Let and , where is a real number. If the largest possible value of is , then the circle , intersects the co-ordinate axes at04 Apr, 2026 (E)Inverse of a Matrix
  9. 9Let and . If and , then among the two statements : (S1): and (S2): ,02 Apr, 2026 (M)Inverse of a Matrix
  10. 10Consider the matrices and . If matrices P and Q are such that and , then the absolute value of the sum of the diagonal elements of is ______02 Apr, 2026 (E)Inverse of a Matrix
  11. 11Let and be three matrices with real entries such that and . If and , then is28 Jan, 2026 (M)Inverse of a Matrix
  12. 12Let and be two matrices such that . Then the sum of all the elements of is28 Jan, 2026 (E)Product of Matrices
  13. 13The number of matrices A, which can be formed using the elements of the set such that the sum of all the diagonal elements of is 5, is24 Jan, 2026 (M)Product of Matrices
  14. 14Let and . If and be such that , then is equal to24 Jan, 2026 (E)Adjoint and its Properties
  15. 15Let and be two square matrices of order 3 such that and . Then the value of is:24 Jan, 2026 (E)Adjoint and its Properties
  16. 16Let , where A is a matrix. If , then is equal to .23 Jan, 2026 (M)Adjoint and its Properties
  17. 17Let and be a matrix such that . Then the sum of the diagonal elements of is equal to .23 Jan, 2026 (E)Types of Matrices
  18. 18If , then the determinant of the matrix is22 Jan, 2026 (M)Inverse of a Matrix
  19. 19Let A be a matrix such that . If and are non-negative integers, then is equal to22 Jan, 2026 (M)Adjoint and its Properties
  20. 20If is a solution of the system of equations , where and , then is equal to :22 Jan, 2026 (E)Adjoint and its Properties
  21. 21For some , let and be such that . Then is equal to .21 Jan, 2026 (M)Product of Matrices
  22. 22For the matrices and , if , then among the following which one is true?21 Jan, 2026 (E)Product of Matrices
  23. 23Let be a solution of , and for some and in . If , then is equal to08 Apr, 2025 (E)Basic Algebra of Matrices
  24. 24Let . If , then is equal to08 Apr, 2025 (E)Adjoint and its Properties
  25. 25The number of singular matrices of order 2 , whose elements are from the set is07 Apr, 2025 (M)Formation and Basic of Matrix
  26. 26Let be a matrix such that , then is equal to07 Apr, 2025 (M)Adjoint and its Properties
  27. 27Let . If for some , , then the sum of the diagonal elements of the matrix is equal to _____ .04 Apr, 2025 (M)Product of Matrices
  28. 28Let the matrix satisfy for . Then the sum of all the elements of is :-04 Apr, 2025 (E)Product of Matrices
  29. 29Let be a matrix of order and . If then is equal to03 Apr, 2025 (M)Adjoint and its Properties
  30. 30Let be the identity matrix of order and for the matrix . Let B be the inverse of the matrix . Then is equal to _____03 Apr, 2025 (E)Adjoint and its Properties
  31. 31Let , such that and . If I denotes identity matrix, then the matrix is:02 Apr, 2025 (M)Basic Algebra of Matrices
  32. 32Let and A be a matrix of order such that and , where is the identity matrix of order . If is , then is equal to :02 Apr, 2025 (M)Adjoint and its Properties
  33. 33Let be a real matrix such that , where I and O are the identity and null matrices, respectively. If , where and are real constants, then is 02 Apr, 2025 (E)Product of Matrices
  34. 34Let \( {A}= [ {a}_{i j} ]= [ {array}{cc} _5 128 & _4 5 \\ _5 8 & _4 25 {array} ]\). If \( {A}_{i j}\) is the cofactor of \( {a}_{i j}, {C}_{29 Jan, 2025 (M)Adjoint and its Properties
  35. 35Let \( {S}= \{ {m} {Z}: {A}^{ {m}^2}+ {A}^{ {m}}=3 {I}- {A}^{-6} \}\), where \( {A}= [ {array}{cc}2 & -1 \\ 1 & 0 {array} ]\). Then \( {n}( 29 Jan, 2025 (M)Product of Matrices
  36. 36Let be a matrix of order , with . If the sum of all the elements in the third row of is , then is equal to :29 Jan, 2025 (E)Product of Matrices
  37. 37Let M denote the set of all real matrices of order and let . Let If , then equals _______28 Jan, 2025 (M)Basic Algebra of Matrices
  38. 38Let and . If and the sum of the diagonal elements of is , where , then is :28 Jan, 2025 (E)Product of Matrices
  39. 39Let be a matrix such that for all nonzero matrices . If , and , then is_____.24 Jan, 2025 (M)Adjoint and its Properties
  40. 40If , and are non-singular matrices of same order, then the inverse of , is equal to23 Jan, 2025 (M)Inverse of a Matrix
  41. 41Let be matrix such that and , then equals :23 Jan, 2025 (E)Product of Matrices
  42. 42Let be a square matrix of order 3 such that and . Then is equal to _______22 Jan, 2025 (M)Adjoint and its Properties
  43. 43For a matrix , let trace denote the sum of all the diagonal elements of . Let be a matrix such that and trace . If , then the value of trace22 Jan, 2025 (E)Adjoint and its Properties
  44. 44Let be a non-singular matrix of order 3 . If and , then is equal to09 Apr, 2024 (M)Adjoint and its Properties
  45. 45Let and be a matrix such that . If and , then is equal to09 Apr, 2024 (E)Inverse of a Matrix
  46. 46Let . If , where is the identity matrix of order , then is equal to08 Apr, 2024 (M)Basic Algebra of Matrices
  47. 47Let . If the sum of the diagonal elements of is , then is equal to_________08 Apr, 2024 (M)Trace of a Matrix
  48. 48If is a square matrix of order 3 such that and , then is equal to :06 Apr, 2024 (E)Adjoint and its Properties
  49. 49Let and be two square matrices of order 3 such that and . Then is equal to :05 Apr, 2024 (M)Adjoint and its Properties
  50. 50Let and . If is the matrix of cofactors of the elements of , then is equal to :05 Apr, 2024 (E)Formation and Basic of Matrix

Frequently Asked Questions

1.How many questions are available for Matrices?

This chapter includes 221 questions compiled from JEE Main papers spanning 2003 to 2026.

2.Are these questions only from JEE Main, or from other exams too?

These are JEE Main questions specifically for the Matrices chapter. Questions from other exams like NTA Abhyas (JEE Main) or JEE Advanced are organised separately under their respective exam sections.

3.Is Matrices an important chapter for JEE Main Mathematics?

Matrices has appeared in 24 of the 25 years of JEE Main papers covered here, with 221 questions across 173 papers - about one per paper it appears in.

4.What is the difficulty level of Matrices questions in JEE Main?

Of the 221 questions analysed for this chapter, 19% are easy, 52% moderate and 29% tough. 2022 had the most, with 32 questions.

5.Which topics in Matrices should I focus on?

These topics have carried the most weightage in Matrices:

  • Product of Matrices - 83 questions (38%)
  • Adjoint and its Properties - 57 questions (26%)
  • Inverse of a Matrix - 26 questions (12%)
  • Product of Matrices has produced the most tough questions (22).
6.Is Matrices's weightage in JEE Main going up or down?

Across all 173 papers analysed, Matrices has averaged about 1.3 questions per paper. In the last three years (2024–2026), that average has stayed about the same, at about 1.1 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.