NUST NET Maths chapter 2: Maths · Matrices and determinants MCQs with answers

By Team Megalecture · Updated 4 Nov 2026

14 exam-style questions on Maths · Matrices and determinants, each with the answer and a short explanation. Ten of them are below to try. The chapter test draws ten fresh questions each time and is marked the moment you finish, with your score by topic.

14 questions · 1 topics · 10 per test

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What chapter 2 covers

Ten Maths · Matrices and determinants questions with answers

Try each one, then open the answer. These ten stay the same; the test draws new ones every time.

1. The value of the determinant with rows [1 2 3], [4 5 6] and [2 4 6] is

  1. A
    0
  2. B
    6
  3. C
    −6
  4. D
    12
Show answer

Answer: A. The third row is 2 times the first row. A determinant with two proportional rows is 0, so no expansion is needed.

2. The value of the determinant with rows [0 a −b], [−a 0 c] and [b −c 0] is

  1. A
    2abc
  2. B
    0
  3. C
    −2abc
  4. D
    a2 + b2 + c2
Show answer

Answer: B. The matrix is skew-symmetric of odd order 3, so its determinant is 0. Expanding confirms it: −a(0 − bc) − b(ac − 0) = abc − abc = 0.

3. A is the matrix with rows [1 2] and [0 1]. Then A3 is the matrix with rows

  1. A
    [1 6] and [0 1]
  2. B
    [1 8] and [0 1]
  3. C
    [3 6] and [0 3]
  4. D
    [1 4] and [0 1]
Show answer

Answer: A. A2 has rows [1 4] and [0 1], and A3 = A2A has rows [1 6] and [0 1]. Cubing each entry (giving 8) is not how matrix powers work.

4. The system x + y + z = 1, 2x + 2y + 2z = 3, x − y + z = 0 is

  1. A
    consistent with a unique solution
  2. B
    inconsistent
  3. C
    consistent with infinitely many solutions
  4. D
    consistent with only the trivial solution
Show answer

Answer: B. Doubling the first equation gives 2x + 2y + 2z = 2, which contradicts 2x + 2y + 2z = 3. So there is no solution: the system is inconsistent.

5. A is the matrix with rows [1 2] and [3 4], and I is the 2 × 2 identity matrix. Then A2 − 5A is equal to

  1. A
    −2I
  2. B
    O (the zero matrix)
  3. C
    5I
  4. D
    2I
Show answer

Answer: D. A2 has rows [7 10] and [15 22]. Subtracting 5A (rows [5 10] and [15 20]) leaves rows [2 0] and [0 2], which is 2I.

6. The value of the determinant with rows [2 −1 0], [1 3 2] and [0 1 1] is

  1. A
    3
  2. B
    1
  3. C
    5
  4. D
    −3
Show answer

Answer: A. Expand along the first row: 2(3 − 2) − (−1)(1 − 0) + 0 = 2 + 1 = 3. Forgetting the minus sign on the middle cofactor gives 2 − 1 = 1.

7. A is a 2 × 2 matrix with |A| = −3. The value of |2At| is

  1. A
    −6
  2. B
    −12
  3. C
    12
  4. D
    −24
Show answer

Answer: B. Transposing does not change a determinant, and multiplying a 2 × 2 matrix by 2 multiplies its determinant by 22 = 4. So |2At| = 4(−3) = −12.

8. The system x + 2y = 3, 2x + ky = 5 has no solution when k is

  1. A
    −4
  2. B
    4
  3. C
    2
  4. D
    6
Show answer

Answer: B. The coefficient determinant k − 4 must be 0, so k = 4. Then doubling the first equation gives 2x + 4y = 6, which contradicts 2x + 4y = 5, so there is no solution.

9. The homogeneous system 2x + y = 0, 4x + 2y = 0 has

  1. A
    infinitely many solutions
  2. B
    only the trivial solution
  3. C
    no solution
  4. D
    exactly two solutions
Show answer

Answer: A. The coefficient determinant 2(2) − 1(4) = 0, so there are non-trivial solutions: every pair with y = −2x works. A homogeneous system always has x = y = 0, so it is never inconsistent.

10. For invertible square matrices A and B of the same order, (AB)−1 is equal to

  1. A
    A−1B−1
  2. B
    BtAt
  3. C
    B−1A−1
  4. D
    AtBt
Show answer

Answer: C. The inverse of a product reverses the order: (AB)(B−1A−1) = A(BB−1)A−1 = I. BtAt is (AB)t, the transpose, not the inverse.

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Maths · Matrices and determinants: questions students ask

How many Maths · Matrices and determinants MCQs are there?

14, each with the answer and a short explanation, across 1 topics: Matrices and determinants. Every chapter test draws ten of them, so you can take it many times.

Is the NUST NET Maths chapter 2 test free?

Yes. The test, the answers and the explanations are free and need no sign-up. Sign in only if you want your scores kept across devices.

How is the chapter test marked?

The moment you press Finish: your score, the right answer and an explanation for every question, and the ones you got wrong saved in My mistakes to retry.

Can I read the explanations in Urdu?

Yes. In practice mode and on your results you can switch the explanations to Urdu.

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