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Mathematics - Matrices

Practise 75 NTA Abhyas (JEE Main) questions on Matrices. Each question shows a quick preview so you can jump straight to the topic you want to revise.

Matrices has been asked in 0 of the 24 years of NTA Abhyas (JEE Main) papers analysed (2002–2025), with 75 questions in all. 100% of them were easy, 0% moderate and 0% tough. Most of its questions came from 2025, with 0 questions that year. In the last three years (2023–2025) it had 0 questions across 63 papers, about 0 per paper.

All of the chapter's questions come from a single topic, Uncategorized.

  1. 1Let A be a non-singular symmetric matrix of order 3 . If A T = A 2 - I , then A - I - 1 is equal to
  2. 2If A = 1 1 3 5 2 6 - 2 - 1 - 3 , where A x = O (where, O is a null matrix and x 15 , x ∈ N ), then which of the following is true?
  3. 3If A 1 , A 2 , A 3 … … . A 20 are 20 skew-symmetric matrices of same order and B = ∑ r = 1 20 2 r A r 2 r + 1 , then the sum of the principa
  4. 4If P = λ 0 1 1 and Q = 4 0 3 1 such that P 2 = Q , then P 3 is equal to
  5. 5Consider A = a 11 a 12 a 21 a 22 and B = 1 1 2 1 such that A B = B A , then the value of a 12 a 21 + a 11 a 22 is
  6. 6Let A = 1 2 3 4 and B = p q r s are two matrices such that A B = B A and r 0 , then the value of 3 p - 3 s 5 q - 4 r is equal to
  7. 7Consider a matrix A = 0 1 2 0 - 3 0 1 1 1 . If 6 A - 1 = a A 2 + b A + c I , where a , b , c ∈ Z and I is an identity matrix, then a + 2 b +
  8. 8If A and B are square matrices of the same order such that A = - B - 1 A B , then A + 3 B 2 is equal to
  9. 9Consider the matrix A = x 2 y z 2 y z x z x 2 y and A A T = 9 I . If T r A 0 and x y z = 1 6 , then the value of x 3 + 8 y 3 + z 3 is equal
  10. 10A and B are two matrices such that the order of A is 3 × 4 , if A ′ B and B A ′ are both defined, then
  11. 11Let A = a i j 3 × 3 be a matrix, where a i j = x i ≠ j 1 i = j ∀ i , j ∈ N i , j ≤ 3 . If C i j be the cofactor of a i j and C 12 + C 23 + C
  12. 12Let A = 2 3 5 7 and B = a 0 0 b where a , b ∈ N . The number of matrices B such that A B = B A , is equal to
  13. 13If A = a b c b c a c a b , a b c = 1 and A T A = I , then the value of a 3 + b 3 + c 3 (where a , b , c 0 and A T is transpose of matrix A )
  14. 14If A is a symmetric and B is a skew symmetric matrix, then which of the following is correct?
  15. 15If A = 2 1 - 1 3 5 2 1 6 1 , then t r A a d j a d j A is equal to (where, t r P denotes the trace of the matrix P i.e. the sum of all the di
  16. 16Let A and B be two matrices such that the order of A is 5 × 7 . If A T B and B A T are both defined, then (where A T is the transpose of mat
  17. 17If A and B are two matrices of order 3 3 satisfying A B = A and B A = B , then A + B 5 is equal to
  18. 18Consider the matrix A = 3 1 - 6 - 2 , then + A 40 is equal to
  19. 19Let the matrix A = 1 1 2 2 and B = A + A 2 + A 3 + A 4 . If B = A , R , then the value of is equal to
  20. 20Let A and B are two non-singular matrices of order 3 such that A + B = 2 I and A - 1 + B - 1 = 3 I , then A B is equal to (where, I is the i
  21. 21The number of matrices X with entries 0 , 2,3 for which the sum of all the principal diagonal elements of X X T is 28 (where X T is the tran
  22. 22Let A = 2 0 7 0 1 0 1 - 2 1 and B = - k 14 k 7 k 0 1 0 k - 4 k - 2 k . If A B = I , where I is an identity matrix of order 3 , then the sum
  23. 23Let A be a matrix of order 3 such that A 2 = 3 A - 2 I where, I is an identity matrix of order 3 . If A 5 = α a + β I, then α β is equal to
  24. 24Let A = 1 2 3 4 1 - 1 2 , then the value of sum of all the elements of A 100 is
  25. 25Let P n be a square matrix of order 3 such that P n = a i j , where a i j = 3 i + j 4 2 n for 1 i 3, 1 j 3 . Then the value of l i m n T r 4
  26. 26Let A = 0 2 y z x y - z x - y z such that A T A = I , then the value of x 2 + y 2 + z 2 is
  27. 27If A = 2 2 9 4 and A 2 + a A + b Ι = O , then a + 2 b is equal to (where, Ι is an identity matrix and O is a null matrix of order 2 respecti
  28. 28Let A = a i j 3 × 3 and B = b i j 3 × 3 , where b i j = a i j + a j i 2 ∀ i , j . Number of such matrices A whose elements are selected from
  29. 29A square matrix A of order 3 satisfies A 2 = Ι - 2 A , where Ι is an identity matrix of order 3 . If A n = 29 A - 12 Ι , then the value of n
  30. 30Let A = 1 - 1 2 - 1 and B = a 1 b - 1 are two matrices. If A + B 2 = A 2 + B 2 , then the value of 3 a + 4 b is equal to
  31. 31Let α , β , γ be three real numbers satisfying α β γ 2 - 1 1 - 1 - 1 - 2 - 1 2 1 = 0 0 0 . If the point A α , β , γ lies on the plane 2 x +
  32. 32If 5 1 4 7 6 2 1 3 5 1 6 - 7 6 2 4 - 7 4 3 5 7 1 1 6 3 4 2 5 2020 = a 1 a 2 a 3 b 1 b 2 b 3 c 1 c 2 c 3 , then the value of 2 a 2 - b 1 + 3
  33. 33Consider a matrix A = a i j 3 × 3 where, a i j = i + 2 j ∀ i j = e v e n 2 i - 3 j ∀ i j = o d d . If b i j is the cofactor of a i j in matr
  34. 34For a matrix A , if A 2 = A and B = I - A , then A B + B A + I - I - A 2 is equal to (where, I is the identity matrix of the same order of m
  35. 35The least positive integral value of k for which cos ⁡ 2 π 7 - sin ⁡ 2 π 7 sin ⁡ 2 π 7 cos ⁡ 2 π 7 k = 1 0 0 1 is
  36. 36If A is a square matrix of order 2 × 2 and B = 1 2 3 4 , such that A B = B A , then A can be
  37. 37The number of all possible symmetric matrices of order 3 × 3 with each entry 1 or 2 and whose sum of diagonal elements is equal to 5 , is
  38. 38If A = 1 - 3 2 k and A 2 - 4 A + 10 I = A , then k is equal to
  39. 39Let A = 2 - 1 1 - 2 3 - 2 - 4 4 - x be a matrix. If A 2 = A, then the value of x is equal to
  40. 40Let A and B are square matrices of order 3 such that A B 2 = B A and B A 2 = A B . If A B 3 = A 3 B m , then m is equal to
  41. 41Let A is a matrix of order 3 × 3 defined as A = a i j 3 × 3 , where a i j = l i m x → 0 1 - c o s i x s i n i x t a n j x ∀ 1 ≤ i , j ≤ 3 ,
  42. 42Let 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 3
  43. 43Let a r = r 4 C r , b r = 4 - r 4 C r , A r = a r 2 3 b r and A = ∑ r = 0 4 A r , then the value of A is equal to
  44. 44Let A = 1 1 3 3 and B = A + A 2 + A 3 + A 4 . If B = A , R , then the value of is equal to
  45. 45If A , B and C are square matrices of same order and Ι is an identity matrix of the same order, such that C 2 = C B + A C and A B = Ι , then
  46. 46Let X = 2 1 0 3 be a matrix. If X 6 = a b c d , then the number of divisors of a + b + 2020 c + d is equal to
  47. 47Let A and B are two non-singular matrices such that A B = B A 2 , B 4 = I and A k = I , then k can be equal to
  48. 48Consider a skew-symmetric matrix A = a b - b c such that a , b and c are selected from the set S = 0, 1 , 2, 3 , . . . . . . . . 12 . If A i
  49. 49For x 0 , let A = x + 1 x 0 0 0 1 x 0 0 0 12 , B = x 6 x 2 + 1 0 0 0 x 4 0 0 0 1 36 be two matrices and C = A B + A B 2 + … + A B n . Then,
  50. 50Let M and N are two non singular matrices of order 3 with real entries such that a d j M = 2 N and a d j N = M . If M N = λ Ι , then the val

Frequently Asked Questions

1.How many questions are available for Matrices?

This chapter includes 75 NTA Abhyas (JEE Main) questions.

2.Are these questions only from NTA Abhyas (JEE Main), or from other exams too?

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

3.What is the difficulty level of Matrices questions in NTA Abhyas (JEE Main)?

Of the 75 questions analysed for this chapter, 100% are easy, 0% moderate and 0% tough. 2025 had the most, with 0 questions.

4.Which topics in Matrices should I focus on?

All of this chapter's questions come from a single topic: Uncategorized.