FSc Part 1 Maths chapter 3: Matrices and determinants MCQs with answers

By Team Megalecture · Updated 4 Nov 2026

27 exam-style questions on 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.

27 questions · 3 topics · 10 per test

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What chapter 3 covers

Ten 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 matrix with rows [x 2] and [8 x] is singular when

  1. A
    x = 4 only
  2. B
    x = ±4
  3. C
    x = ±2
  4. D
    x = 16
Show answer

Answer: B. |A| = x2 − 16 = 0, so x = 4 or x = −4. Forgetting the negative root gives only 4.

2. For the matrix with rows [2 1 3], [4 5 6] and [7 8 9], the cofactor A12 is

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

Answer: A. The minor M12 deletes row 1 and column 2: (4)(9) − (6)(7) = 36 − 42 = −6. A12 = (−1)1+2M12 = 6.

3. If two rows of a determinant are interchanged, the value of the determinant

  1. A
    is unchanged
  2. B
    changes sign
  3. C
    becomes zero
  4. D
    is doubled
Show answer

Answer: B. Each interchange of two rows (or columns) multiplies the determinant by −1.

4. If two rows of a determinant are identical, its value is

  1. A
    0
  2. B
    1
  3. C
    −1
  4. D
    the product of the diagonal elements
Show answer

Answer: A. Swapping the two equal rows changes the sign but leaves the determinant the same, so |A| = −|A| and |A| = 0.

5. A is a 3 × 3 matrix with |A| = 5. The value of |2A| is

  1. A
    20
  2. B
    10
  3. C
    40
  4. D
    25
Show answer

Answer: C. Multiplying A by 2 multiplies every one of the 3 rows by 2, so |2A| = 23|A| = 8 × 5 = 40.

6. A square matrix A is called singular if

  1. A
    A has no zero entries
  2. B
    |A| = 1
  3. C
    A = At
  4. D
    |A| = 0
Show answer

Answer: D. A singular matrix has zero determinant and so has no inverse. Non-singular means |A| ≠ 0.

7. When the system AX = B is solved by the matrix inverse method, X is equal to

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

Answer: C. Pre-multiply both sides by A−1: A−1AX = A−1B, so X = A−1B. Order matters because matrix multiplication is not commutative.

8. The inverse of the matrix with rows [2 1] and [5 3] is the matrix with rows

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

Answer: B. |A| = 6 − 5 = 1. Swap the diagonal entries and change the signs of the other two, then divide by 1: rows [3 −1], [−5 2].

9. For matrices A and B of suitable orders, (AB)t is equal to

  1. A
    (BA)t
  2. B
    AtBt
  3. C
    BA
  4. D
    BtAt
Show answer

Answer: D. The transpose of a product is the product of the transposes in reverse order: (AB)t = BtAt.

10. A square matrix A with complex entries is Hermitian when

  1. A
    At = A
  2. B
    (Ā)t = A
  3. C
    (Ā)t = −A
  4. D
    Ā = A
Show answer

Answer: B. Hermitian means the conjugate transpose equals A. At = A is symmetric, (Ā)t = −A is skew-Hermitian, and Ā = A means the entries are real.

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Ways to practise this chapter

Matrices and determinants: questions students ask

How many Matrices and determinants MCQs are there?

27, each with the answer and a short explanation, across 3 topics: Matrices and matrix algebra, Determinants, Systems of linear equations. Every chapter test draws ten of them, so you can take it many times.

Is the FSc Part 1 Maths chapter 3 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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