Matrices — Class 12 MCQs with Answers

Matrices — important questions & MCQs with answers (Class 12 Mathematics)

14 solved questions from this chapter's difficulty levels, each with its answer and explanation. The other 76 are timed and scored when you sign in.

1. Q1Easy

   Order of matrix with 2 rows, 3 columns:

   A.6

   B.3 × 2

   C.2 × 3✓ Correct

   D.5

   Answer: C. 2 × 3

   Explanation: Matrix order is always written rows × columns, so 2 rows and 3 columns gives 2×3 — not 3×2, which swaps the convention.

2. Q2Easy

   A row matrix has:

   A.Same rows and columns

   B.1 column

   C.1 row✓ Correct

   D.No restriction

   Answer: C. 1 row

   Explanation: A row matrix has exactly 1 row and any number of columns — don't confuse it with a column matrix, which instead has exactly 1 column.

3. Q3Easy

   Two matrices can be added if:

   A.Square

   B.Same number of rows

   C.They have the same order✓ Correct

   D.Same number of columns

   Answer: C. They have the same order

   Explanation: Two matrices can be added only if they have the same order — same rows AND same columns; matching rows alone or columns alone isn't enough.

4. Q4Easy

   Transpose A^T of matrix A:

   A.Multiplies by −1

   B.Adds 1 to entries

   C.Interchanges rows and columns✓ Correct

   D.Inverts

   Answer: C. Interchanges rows and columns

   Explanation: The transpose Aᵀ interchanges the rows and columns of A — row i becomes column i; it does not multiply by −1, add 1, or invert A.

5. Q5Easy

   A square matrix A is symmetric if:

   A.A is identity

   B.A^T = −A

   C.A is diagonal

   D.A^T = A✓ Correct

   Answer: D. A^T = A

   Explanation: By definition, a square matrix A is symmetric when Aᵀ = A; Aᵀ = −A instead defines a skew-symmetric matrix — don't mix up the sign.

6. Q6Easy

   The trace of the matrix [[2, 5], [1, 3]] is:

   A.5✓ Correct

   B.2

   C.6

   D.11

   Answer: A. 5

   Explanation: The trace is the sum of the diagonal elements, 2 + 3 = 5.

7. Q7Medium

   (A')' =

   A.A²

   B.−A

   C.A✓ Correct

   D.A⁻¹

   Answer: C. A

   Explanation: Transposing swaps rows and columns; doing it twice undoes the swap and returns the original matrix, so (Aᵀ)ᵀ = A, not A² or −A.

8. Q8Medium

   In matrix A = [a_ij], a_23 represents the element in:

   A.First position

   B.Row 3, column 2

   C.Row 2, column 2

   D.Row 2, column 3✓ Correct

   Answer: D. Row 2, column 3

   Explanation: In a_ij, the first subscript i is the row and the second j is the column, so a₂₃ is the entry in row 2, column 3.

9. Q9Medium

   For AB to be defined, columns of A must equal:

   A.Rows of B✓ Correct

   B.Columns of B

   C.Rows of A

   D.Determinant

   Answer: A. Rows of B

   Explanation: For AB to exist, the inner dimensions must match: columns of A equal rows of B, since (m×n)(n×p) → m×p; the column count of B is irrelevant here.

10. Q10Medium

    Transpose of [[1, 2, 3], [4, 5, 6]]:

    A.[[4, 5, 6], [1, 2, 3]]

    B.[[1, 2, 3], [4, 5, 6]]

    C.[[3, 2, 1], [6, 5, 4]]

    D.[[1, 4], [2, 5], [3, 6]]✓ Correct

    Answer: D. [[1, 4], [2, 5], [3, 6]]

    Explanation: Transposing swaps rows and columns: the first row (1,2,3) becomes the first column, giving [[1,4],[2,5],[3,6]] — a 3×2 matrix, not another 2×3 arrangement.

11. Q11Medium

    For symmetric matrix A: a_ij =

    A.−a_ji

    B.a_ji✓ Correct

    C.Always 0

    D.Always non-zero

    Answer: B. a_ji

    Explanation: For a symmetric matrix, the entry in row i, column j equals the entry in row j, column i: a_ij = a_ji.

12. Q12Hard

    Matrix A is orthogonal if:

    A.A² = I

    B.A^T = −A

    C.A · A^T = I✓ Correct

    D.det A = 0

    Answer: C. A · A^T = I

    Explanation: A matrix A is orthogonal by definition when A·Aᵀ = I, i.e. its transpose equals its inverse — not merely A² = I or a zero determinant.

13. Q13Hard

    Symmetric matrix:

    A.A = 0

    B.A' = −A

    C.A·A' = 0

    D.A' = A✓ Correct

    Answer: D. A' = A

    Explanation: A symmetric matrix satisfies Aᵀ = A — it equals its own transpose; a matrix with Aᵀ = −A is instead called skew-symmetric, a different sign entirely.

14. Q14Hard

    For any two matrices A and B for which AB is defined, (AB)ᵀ equals:

    A.BA

    B.AᵀBᵀ

    C.AB

    D.BᵀAᵀ✓ Correct

    Answer: D. BᵀAᵀ

    Explanation: The transpose of a product is the product of the transposes taken in the reverse order.

Matrices — FAQs

More Class 12 Mathematics chapters

• 01Relations and Functions
• 02Inverse Trigonometric Functions
• 04Determinants
• 05Continuity and Differentiability
• 06Application of Derivatives
• 07Integrals

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