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Mathematics - Matrices

Practise 41 JEE Advanced previous year questions on Matrices, compiled from papers spanning 2006 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 Advanced tests.

Matrices has been asked in 17 of the 27 years of JEE Advanced papers analysed (2000–2026), with 41 questions in all. 29% of them were easy, 46% moderate and 24% tough. Most of its questions came from 2011, with 5 questions that year. In the last three years (2024–2026) it had 7 questions across 6 papers, about 1.2 per paper.

The chapter's 8 topics are not weighted equally: Product of Matrices (13 questions, 32%), Inverse of a Matrix (6 questions, 15%), and Basic Algebra of Matrices (5 questions, 12%) have been asked the most. Product of Matrices has also led over the last five years, with 5 questions. Symmetric & Skew Symmetric Matrices has produced the most tough questions (3).

  1. 1Which one of the following matrices can be obtained by performing elementary row transformations on the identity matrix?2026 (Paper 1)Inverse of a Matrix
  2. 2Consider the matrix . Let and be integers such that and . Then which of the following statements is (are) TRUE?2026 (Paper 1)Product of Matrices
  3. 3For real numbers and , consider the matrix . Suppose that , where is the transpose of the matrix , and is the identity matrix. Let , and . M2026 (Paper 1)Types of Matrices
  4. 4Let denote the set of all real numbers and let . Consider the matrices and . Let be real numbers such that . Let . Then which of the followi2026 (Paper 2)Product of Matrices
  5. 5Consider the matrix, Let the transpose of a matrix be denoted by . Then the number of invertible matrices Q with integer entries, such that 2025 (Paper 1)Types of Matrices
  6. 6Let and . Let for some non-zero real numbers , and , for which there is matrix with all entries being non-zero real numbers, such that . The2025 (Paper 2)Product of Matrices
  7. 7Let and be the distinct roots of the equation . Consider the set . For a matrix , define and for and . Match each entry in List-I to the cor2024 (Paper 1)Symmetric & Skew Symmetric Matrices
  8. 8Let M = a i j , i , j { 1 , 2 , 3 } , be the 3 3 matrix such that a i j = 1 if j + 1 is divisible by i , otherwise a i j = 0 . Then which of2023 (Paper 2)Inverse of a Matrix
  9. 9Let R = a 3 b c 2 d 0 5 0 : a , b , c , d 0 , 3 , 5 , 7 , 11 , 13 , 17 , 19 . Then the number of invertible matrices in R is2023 (Paper 2)Formation and Basic of Matrix
  10. 10Let be a real number. Consider the matrix A = 0 1 2 1 - 2 3 1 - 2 . If A 7 - - 1 A 6 - A 5 is a singular matrix, then the value of 9 is ____2022 (Paper 2)Product of Matrices
  11. 11If M = 5 2 3 2 - 3 2 - 1 2 , then which of the following matrices is equal to M 2022 ?2022 (Paper 2)Product of Matrices
  12. 12For any 3 3 matrix M , let | M | denote the determinant of M . Let E = 1 2 3 2 3 4 8 13 18 , P = 1 0 0 0 0 1 0 1 0 F = 1 3 2 8 18 13 2 4 3 I2021 (Paper 1)Basic Algebra of Matrices
  13. 13For any 3 3 matrix M , let | M | denote the determinant of M . Let I be the 3 3 identity matrix. Let E and F be two 3 3 matrices such that (2021 (Paper 1)Inverse of a Matrix
  14. 14Let M be a 3 3 invertible matrix with real entries and let I denote the 3 3 identity matrix. M 1 = a d j a d j M , then which of the followi2020 (Paper 1)Adjoint and its Properties
  15. 15The trace of a square matrix is defined to be the sum of its diagonal entries. If A is a 2 2 matrix such that the trace of A is 3 and the tr2020 (Paper 2)Trace of a Matrix
  16. 16Let M = sin 4 - 1 - sin 2 1 + cos 2 cos 4 = I + M - 1 , where = and = are real number, and I is the 2 2 identity matrix. If * is the minimum2019 (Paper 1)Inverse of a Matrix
  17. 17Let M = 0 1 a 1 2 3 3 b 1 and a d j M = - 1 1 - 1 8 - 6 2 - 5 3 - 1 where a and b are real numbers. Which of the following options is/are co2019 (Paper 1)Adjoint and its Properties
  18. 18Let P 1 = I = 1 0 0 0 1 0 0 0 1 , P 2 = 1 0 0 0 0 1 0 1 0 , P 3 = 0 1 0 1 0 0 0 0 1 , P 4 = 0 1 0 0 0 1 1 0 0 , P 5 = 0 0 1 1 0 0 0 1 0 , P 2019 (Paper 2)Trace of a Matrix
  19. 19The number of 3 × 3 matrices M with entries from { 0,1 , 2 } , such that the sum of the diagonal elements of M T M is 5 , are2017 (Paper 2)Product of Matrices
  20. 20Let P = 3 - 1 - 2 2 0 3 - 5 0 , where R , Suppose Q = q i j is a matrix such that P Q = k I , where k R , k 0 and I is the identity matrix o2016 (Paper 1)Adjoint and its Properties
  21. 21Let z = - 1 + 3 i 2 , where i = - 1 , and r , s 1 , 2 , 3 . Let P = - z r z 2 s z 2 s z r and I be the identity matrix of order 2. Then the 2016 (Paper 1)Product of Matrices
  22. 22Let P = 1 0 0 4 1 0 16 4 1 and I be the identity matrix of order 3 . If Q = q i j is a matrix such that P 50 - Q = I , then the value of q 32016 (Paper 2)Product of Matrices
  23. 23Let X a n d Y be two arbitrary, 3 3 , non - zero, skew - symmetric matrices and Z be an arbitrary 3 3 , non - zero, symmetric matrix. Then w2015 (Paper 1)Symmetric & Skew Symmetric Matrices
  24. 24Let M be a 2 2 symmetric matrix with integer entries. Then M is invertible if2014 (Paper 1)Inverse of a Matrix
  25. 25Let M and N be two 3 3 matrices such that MN = NM. Further, if M N 2 and M 2 = N 4 , then2014 (Paper 1)Basic Algebra of Matrices
  26. 26For 3 x 3 matrices M and N, which of the following statement(s) is (are) not correct?2013 (Paper 1)Symmetric & Skew Symmetric Matrices
  27. 27Let be a complex cube root of unity with 1 and P = p ij be a n x n matrix with p ij = i + j . Then P 2 0 , when n =2013 (Paper 2)Basic Algebra of Matrices
  28. 28If is a matrix such that , where is the transpose of and is the identity matrix, then there exists a column matrix such that2012 (Paper 2)Basic Algebra of Matrices
  29. 29If the adjoint of a matrix is , then the possible value(s) of the determinant of is (are)2012 (Paper 2)Adjoint and its Properties
  30. 30Let and be two non-singular skew-symmetric matrices such that . If denotes the transpose of , then is equal to2011 (Paper 1)Symmetric & Skew Symmetric Matrices
  31. 31Paragraph: Let , b and be three real numbers satisfying Question: If the point , with reference to Eq. (E), lies on the plane , then the val2011 (Paper 1)Product of Matrices
  32. 32Paragraph: Let , b and be three real numbers satisfying Question: Let , with and satisfying Eq. (E). If and are the roots of the quadratic e2011 (Paper 1)Product of Matrices
  33. 33Let be a cube root of unity and be the set of all non-singular matrices of the form , where each of and is either or . Then, the number of d2011 (Paper 2)Formation and Basic of Matrix
  34. 34Then, the sum of the diagonal entries of is2011 (Paper 2)Product of Matrices
  35. 35The number of matrices whose entries are either 0 or 1 and for which the system has exactly two distinct solutions, is2010 (Paper 1)Basic Algebra of Matrices
  36. 36Paragraph: Let be an odd prime number and be the following set of matrices Question: The number of in such that is either symmetric or skew-2010 (Paper 1)Symmetric & Skew Symmetric Matrices
  37. 37Paragraph: Let be an odd prime number and be the following set of matrices Question: The number of in such that the trace of is not divisibl2010 (Paper 1)Trace of a Matrix
  38. 38Paragraph: Let be an odd prime number and be the following set of matrices Question: The number of in such that is not divisible by , is2010 (Paper 1)Trace of a Matrix
  39. 39Paragraph: Read the following passage and answer the questions. Question: The value of is2006Product of Matrices
  40. 40Paragraph: Read the following passage and answer the questions. Question: The value of the elements of is2006Inverse of a Matrix
  41. 41Paragraph: Read the following passage and answer the questions. Question: The value of is2006Product of Matrices

Frequently Asked Questions

1.How many questions are available for Matrices?

This chapter includes 41 questions compiled from JEE Advanced papers spanning 2006 to 2026.

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

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

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

Matrices has appeared in 17 of the 21 years of JEE Advanced papers covered here, with 41 questions across 24 papers - about 2 per paper it appears in.

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

Of the 41 questions analysed for this chapter, 29% are easy, 46% moderate and 24% tough. 2011 had the most, with 5 questions.

5.Which topics in Matrices should I focus on?

These topics have carried the most weightage in Matrices:

  • Product of Matrices - 13 questions (32%)
  • Inverse of a Matrix - 6 questions (15%)
  • Basic Algebra of Matrices - 5 questions (12%)
  • Symmetric & Skew Symmetric Matrices has produced the most tough questions (3).
6.Is Matrices's weightage in JEE Advanced going up or down?

Across all 24 papers analysed, Matrices has averaged about 1.7 questions per paper. In the last three years (2024–2026), that average has fallen, at about 1.2 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.