Matrices Practice Questions

Class 12 · Mathematics · 2241 free MCQs with instant results and detailed explanations.

2241

Total

697

Easy

1090

Medium

454

Hard

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Topics in Matrices

Symmetric and Skew Symmetric 627

Transpose 493

Operations on Matrices 493

Types of Matrices 628

Sample Questions from Matrices

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Easy

Which of the following matrices is a diagonal matrix?

A. [[2, 0], [0, 3]]

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

C. [[0, 1], [1, 0]]

D. [[1, 2], [0, 0]]

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Correct Answer: A

A diagonal matrix has non-zero elements only on its main diagonal. Option A fits this definition.

Easy

What type of matrix is represented by the equation A + A^T = 0?

A. Symmetric matrix

B. Skew-symmetric matrix

C. Zero matrix

D. Identity matrix

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Correct Answer: B

A matrix A is skew-symmetric if A^T = -A. The equation given indicates that A is skew-symmetric.

Easy

If matrix B is a 3x3 identity matrix, which of the following statements is true?

A. B has all elements equal to 1

B. B is non-invertible

C. The determinant of B is 1

D. B has no eigenvalues

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Correct Answer: C

The determinant of an identity matrix is always 1, regardless of its size.

Medium

Which of the following matrices is a square matrix?

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

B. [1, 0; 0, 1]

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

D. [1, 2; 3, 4; 5]

Show Answer & Explanation

Correct Answer: B

A square matrix has the same number of rows and columns, which is true for option B.

Medium

If A is a 2x3 matrix and B is a 3x2 matrix, what is the order of the product AB?

A. 2x2

B. 3x3

C. 2x3

D. 3x2

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Correct Answer: A

The order of the product of two matrices is determined by the outer dimensions, hence 2x2.

Medium

Which of the following statements is true for a diagonal matrix?

A. All elements are zero

B. Non-diagonal elements are non-zero

C. Only diagonal elements can be non-zero

D. It must be a square matrix with all same values

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Correct Answer: C

A diagonal matrix has non-zero elements only on its diagonal, and all other elements are zero.

Medium

If A = [2, 0; 0, 3], what is A^2?

A. [4, 0; 0, 9]

B. [2, 0; 0, 3]

C. [5, 0; 0, 6]

D. [0, 0; 0, 0]

Show Answer & Explanation

Correct Answer: A

Squaring a diagonal matrix involves squaring each of its diagonal elements.

Hard

If A is a 3x3 matrix defined as A = [[0, 1, 0], [0, 0, 1], [1, 0, 0]], what type of matrix is A?

A. Cyclic

B. Symmetric

C. Diagonal

D. Null

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Correct Answer: A

A is a cyclic matrix as the rows are cyclic permutations of each other.

Hard

Which of the following matrices is not symmetric?

A. [[2, 3], [3, 4]]

B. [[1, 0], [0, 1]]

C. [[1, 2], [0, 1]]

D. [[5, 1], [1, 5]]

Show Answer & Explanation

Correct Answer: C

Matrix C is not symmetric because A[i][j] ≠ A[j][i] for i=1, j=2.

Q10

Hard

A square matrix is skew-symmetric if A^T = -A. Which of the following is skew-symmetric?

A. [[0, 2], [-2, 0]]

B. [[1, -1], [1, 1]]

C. [[0, 1], [1, 0]]

D. [[2, 0], [0, 2]]

Show Answer & Explanation

Correct Answer: A

Matrix A is skew-symmetric as its transpose equals its negative.

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Matrices — Class 12 Mathematics Practice Questions Online

This page contains 2241 practice MCQs for the chapter Matrices in Class 12 Mathematics. The questions are organized by difficulty — 697 easy, 1090 medium, 454 hard — so you can choose the right level for your preparation.

Every question includes a detailed explanation to help you understand the concept, not just memorize answers. Take a timed quiz to simulate exam conditions, or practice at your own pace with no time limit. This chapter covers 4 topics, giving you comprehensive coverage of the entire chapter.