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Mathematics - Matrices

Practise 153 NDA previous year questions on Matrices, compiled from papers spanning 2010 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 NDA tests.

Matrices has been asked in 17 of the 21 years of NDA papers analysed (2006–2026), with 153 questions in all. 36% of them were easy, 63% moderate and 1% tough. Most of its questions came from 2017, with 14 questions that year. In the last three years (2024–2026) it had 26 questions across 5 papers, about 5.2 per paper.

The chapter's 8 topics are not weighted equally: Inverse of a Matrix (48 questions, 31%), Product of Matrices (47 questions, 31%), and Adjoint and its Properties (20 questions, 13%) have been asked the most. Inverse of a Matrix has also led over the last five years, with 12 questions. Inverse of a Matrix has produced the most tough questions (1).

  1. 1Consider the following statements : I. If matrix is symmetric, then its inverse is also a symmetric matrix. II. If matrix is singular, then 2026 (Phase 1)Inverse of a Matrix
  2. 2If where is a natural number, then what is equal to ?2026 (Phase 1)Expansion of Determinants
  3. 3If is the transpose of a matrix , then which of the following is/are correct ? I. if is symmetric. II. if is anti-symmetric. Select the answ2026 (Phase 1)Symmetric & Skew Symmetric Matrices
  4. 4If is a square matrix such that , then how many values of are possible ?2026 (Phase 1)Product of Matrices
  5. 5If , then which one of the following is a value of ?2025 (Phase 1)Product of Matrices
  6. 6If where , , are integers, is an orthogonal matrix, then what is the value of ?2025 (Phase 1)Types of Matrices
  7. 7If , then what is equal to?2025 (Phase 1)Basic Algebra of Matrices
  8. 8If , then what is equal to?2025 (Phase 1)Product of Matrices
  9. 9If where , , are integers, is an orthogonal matrix, then what is equal to?2025 (Phase 1)Types of Matrices
  10. 10What is the value of the determinant of the inverse of the matrix ?2025 (Phase 2)Inverse of a Matrix
  11. 11Consider the following in respect of non-singular matrices and : I. II. , where is the identity matrix III. How many of the above are correc2025 (Phase 2)Inverse of a Matrix
  12. 12For the following two (02) items: Let . What is the value of the determinant of the matrix ?2025 (Phase 2)Product of Matrices
  13. 13For the following two (02) items: Let . What is equal to?2025 (Phase 2)Adjoint and its Properties
  14. 14Consider the following statements about the matrix : Statement-I: The inverse of does not exist. Statement-II: is non-singular. Which one of2025 (Phase 2)Inverse of a Matrix
  15. 15Let A and B be matrices of order . If and , then what is the value of ?2024 (Phase 1)Adjoint and its Properties
  16. 16Consider the following statements in respect of two non-singular matrices A and B of the same order : 1. 2. 3. is a null matrix of order How2024 (Phase 1)Adjoint and its Properties
  17. 17Consider the following statements in respect of a non-singular matrix A of order : 1. 2. If , then A is identity matrix of order 3. If , the2024 (Phase 1)Adjoint and its Properties
  18. 18Consider the following statements in respect of a skew-symmetric matrix A of order 3: 1. All diagonal elements are zero. 2. The sum of all t2024 (Phase 1)Symmetric & Skew Symmetric Matrices
  19. 19What is the number of different matrices, each having 4 entries that can be formed using , 4 (repetition is allowed)?2024 (Phase 1)Formation and Basic of Matrix
  20. 20If , then which of the following statements is/are correct? 1. 2. A is skew-symmetric matrix 3. Select the correct answer using the code giv2024 (Phase 1)Inverse of a Matrix
  21. 21Let X be a matrix of order be a matrix of order and Z be a matrix of order . Which of the following statements are correct? A. is defined an2024 (Phase 2)Product of Matrices
  22. 22Let and be two square matrices of same order. If is a null matrix, then which one of the following is correct?2024 (Phase 2)Inverse of a Matrix
  23. 23Consider the following in respect of the matrices A. PQ is null a matrix. B. QP is an identity matrix of order 3. C. which of the above is/a2024 (Phase 2)Product of Matrices
  24. 24If P is a skew-symmetric matrix of order 3 , then what is equal to?2024 (Phase 2)Symmetric & Skew Symmetric Matrices
  25. 25Paragraph: Let Question: What is equal to?2024 (Phase 2)Adjoint and its Properties
  26. 26Paragraph: Let Question: What is equal to?2024 (Phase 2)Inverse of a Matrix
  27. 27Let A be a matrix of order and . If , then what is the value of ?2023 (Phase 1)Adjoint and its Properties
  28. 28Let and be symmetric matrices of same order, then which one of the following is correct regarding ? 1. Its diagonal entries are equal but no2023 (Phase 1)Symmetric & Skew Symmetric Matrices
  29. 29Consider the following statements in respect of square matrices each of same order : 1. if is non-singular 2. If for every column matrix X h2023 (Phase 1)Inverse of a Matrix
  30. 30If , then what is value of , where I is the identity matrix?2023 (Phase 2)Adjoint and its Properties
  31. 31If and are square matrices of order 3 and , then what is the value of ?2023 (Phase 2)Inverse of a Matrix
  32. 32If , then which one of the following statements is correct?2023 (Phase 2)Symmetric & Skew Symmetric Matrices
  33. 33If , then which of the following statements are correct? 1. will always be singular for any positive integer . 2. will always be a diagonal 2023 (Phase 2)Types of Matrices
  34. 34If , then what is the value of2023 (Phase 2)Adjoint and its Properties
  35. 35If , then what is equal to?2023 (Phase 2)Product of Matrices
  36. 36Consider the following in respect of the matrices: and 1. 2. 3. Which of the above statements is/are correct?2022 (Phase 1)Basic Algebra of Matrices
  37. 37If , then what is equal to? where is the identify matrix.2022 (Phase 1)Adjoint and its Properties
  38. 38Let be a non-singular matrix and . Which of the following statements is/are correct? 1. 2. is a scalar matrix 3. can be a null matrix Select2022 (Phase 1)Adjoint and its Properties
  39. 39Consider the following statements in respect of square matrices and of same order: 1. If is a null matrix, then at last one of and is a null2022 (Phase 1)Product of Matrices
  40. 40If is the identity matrix of order 3 and is its transpose, then what is the value of the determinant of the matrix ?2022 (Phase 1)Inverse of a Matrix
  41. 41Let and be non-singular matrices of the same order such that and . Which of the following statements is/are correct? 1. 2. Select the correc2022 (Phase 1)Inverse of a Matrix
  42. 42If , then which of the following are correct? 1. is a null matrix 2. is a null matrix 3. is a null matrix Select the correct answer using th2022 (Phase 2)Inverse of a Matrix
  43. 43If is a matrix of order is a matrix of order and is a matrix of order , then which of the following are correct? 1. is a square matrix havin2022 (Phase 2)Product of Matrices
  44. 44Paragraph: Let and where is symmetric matrix and is skew-symmetric matrix. Question: What is equal to?2022 (Phase 2)Symmetric & Skew Symmetric Matrices
  45. 45Paragraph: Let and where is symmetric matrix and is skew-symmetric matrix. Question: What is equal to ?2022 (Phase 2)Symmetric & Skew Symmetric Matrices
  46. 46If and are two matrices such that is of order , then which one of the following is correct?2021 (Phase 1)Product of Matrices
  47. 47How many matrices of different orders are possible with elements comprising all prime numbers less than 30 ?2021 (Phase 1)Formation and Basic of Matrix
  48. 48If and are square matrices of order 2 such that , then which one of the following is correct?2021 (Phase 1)Product of Matrices
  49. 49If where , then what is equal to? where is the identity matrix.2021 (Phase 2)Product of Matrices
  50. 50How many distinct matrices exist with all four entries taken from ?2021 (Phase 2)Formation and Basic of Matrix

Frequently Asked Questions

1.How many questions are available for Matrices?

This chapter includes 153 questions compiled from NDA papers spanning 2010 to 2026.

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

These are NDA 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 NDA Mathematics?

Matrices has appeared in 17 of the 17 years of NDA papers covered here, with 153 questions across 32 papers - about 5 per paper it appears in.

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

Of the 153 questions analysed for this chapter, 36% are easy, 63% moderate and 1% tough. 2017 had the most, with 14 questions.

5.Which topics in Matrices should I focus on?

These topics have carried the most weightage in Matrices:

  • Inverse of a Matrix - 48 questions (31%)
  • Product of Matrices - 47 questions (31%)
  • Adjoint and its Properties - 20 questions (13%)
  • Inverse of a Matrix has produced the most tough questions (1).
6.Is Matrices's weightage in NDA going up or down?

Across all 32 papers analysed, Matrices has averaged about 4.8 questions per paper. In the last three years (2024–2026), that average has stayed about the same, at about 5.2 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.