Matrices and Determinants Practice Questions

JEE · Mathematics · 1781 free MCQs with instant results and detailed explanations.

1781

Total

377

Easy

786

Medium

618

Hard

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Topics in Matrices and Determinants

Types of Matrices 288

Operations 200

Inverse of a Matrix 207

Cramer's Rule 231

Matrix Operations 218

Determinants 212

Adjoint and Inverse 201

System of Linear Equations 224

Sample Questions from Matrices and Determinants

Here are 10 sample questions. Start a quiz to get randomized questions with scoring.

Easy

If matrix A is a 2x2 matrix given by A = [[2, 3], [1, 4]], what is the result of the operation 2A?

A. [[4, 6], [2, 8]]

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

C. [[2, 3], [2, 4]]

D. [[1, 1.5], [0.5, 2]]

Show Answer & Explanation

Correct Answer: A

Multiplying a matrix by a scalar involves multiplying each element of the matrix by that scalar.

Easy

Consider two matrices C = [[1, 2], [3, 4]] and D = [[5, 6], [7, 8]]. What is the sum of C and D?

A. [[6, 8], [10, 12]]

B. [[5, 8], [10, 12]]

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

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

Show Answer & Explanation

Correct Answer: A

To find the sum of two matrices, add their corresponding elements.

Easy

What is the result of adding two matrices A and B of the same order?

A. A matrix of the same size with corresponding elements added

B. A scalar value

C. A matrix of half the size

D. A null matrix

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Correct Answer: A

Matrix addition is performed by adding corresponding elements from two matrices of the same order.

Medium

If A = [[2, -1], [3, 4]], then find the value of |A|.

A. 11

B. -11

C. 5

D. 10

Show Answer & Explanation

Correct Answer: A

The determinant of A is calculated as (2*4) - (-1*3) = 8 + 3 = 11.

Medium

For matrices A = [[1, 2], [3, 4]] and B = [[5, 6], [7, 8]], what is A + B?

A. [[6, 8], [10, 12]]

B. [[8, 10], [12, 14]]

C. [[4, 6], [10, 12]]

D. [[12, 14], [16, 18]]

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Correct Answer: A

To add two matrices, add corresponding elements: A + B = [[1+5, 2+6], [3+7, 4+8]] = [[6, 8], [10, 12]].

Medium

Given two matrices A and B, if |A| = 2 and |B| = 3, what is |AB|?

A. 6

B. 5

C. 1

D. 0

Show Answer & Explanation

Correct Answer: A

The determinant of the product of two matrices is the product of their determinants: |AB| = |A| * |B| = 2 * 3 = 6.

Medium

For the matrices A = [[1, 0], [0, 1]] and B = [[0, 1], [1, 0]], what is A + B?

A. [[1, 1], [1, 1]]

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

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

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

Show Answer & Explanation

Correct Answer: A

Adding matrices involves adding corresponding elements: [[1+0, 0+1], [0+1, 1+0]] results in [[1, 1], [1, 1]].

Hard

If A is a 3x3 matrix with elements a_ij = i + j, where i, j = 1, 2, 3, what is the value of the determinant of A?

A. 0

B. 6

C. 12

D. 18

Show Answer & Explanation

Correct Answer: A

The rows of the matrix are linearly dependent, hence the determinant is 0.

Hard

Find the eigenvalues of the matrix A = [[4, 1], [2, 3]].

A. 5, 2

B. 3, 4

C. 2, 5

D. 1, 6

Show Answer & Explanation

Correct Answer: A

The eigenvalues are found using the characteristic polynomial |A - λI| = 0. This gives λ^2 - 7λ + 10 = 0, solving gives λ = 5, 2.

Q10

Hard

What is the rank of the matrix B = [[1, 2, 1], [2, 4, 2], [3, 6, 3]]?

A. 1

B. 2

C. 3

D. 0

Show Answer & Explanation

Correct Answer: A

All rows are multiples of the first row, hence there is only 1 linearly independent row.

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Matrices and Determinants — JEE Mathematics Practice Questions Online

This page contains 1781 practice MCQs for the chapter Matrices and Determinants in JEE Mathematics. The questions are organized by difficulty — 377 easy, 786 medium, 618 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 8 topics, giving you comprehensive coverage of the entire chapter.