COMEDK UGET 2026 Matrices and Determinants Practice Questions with Solutions

Matrices and Determinants is one of the most important and scoring chapters in the Mathematics section of the COMEDK UGET exam. For COMEDK UGET 2026 aspirants, practicing a good number of questions from this chapter is essential because the exam frequently includes direct concept-based problems from matrices and determinants. Solving practice questions with solutions helps students understand the pattern of questions, strengthen their conceptual clarity, and improve speed and accuracy. Since COMEDK is a time-bound exam, regular practice of such questions also helps students become familiar with calculation techniques and shortcuts needed to solve problems quickly.

In the COMEDK Mathematics syllabus, Matrices and Determinants belong to the Algebra section and carry a significant weightage in the exam. Based on previous exam trends, students can expect around 4–5 questions from this chapter, contributing approximately 6–8% of the total Mathematics paper. Because of this consistent presence in the exam, it becomes a high-priority topic for students aiming to score well in the Mathematics section. Questions are generally objective in nature and focus on applying formulas, properties, and conceptual understanding rather than lengthy derivations.

Several important areas from matrices and determinants are commonly tested in COMEDK UGET . Some of the key topics include types of matrices (identity, zero, symmetric, skew-symmetric), matrix operations such as addition and multiplication, transpose of a matrix, scalar multiplication, properties of matrices, inverse of a matrix, adjoint of a matrix, and determinant properties. Questions are also frequently asked from concepts such as evaluating determinants, solving matrix equations, finding the inverse using adjoint, and applying determinant properties to simplify expressions. In many cases, the exam tests conceptual understanding through straightforward calculations or property-based problems.

Looking at the trend of the last 3–4 years of COMEDK papers, questions from Matrices and Determinants have generally been easy to moderate in difficulty level. Most questions are directly based on standard formulas, determinant properties, or simple matrix operations, making them relatively scoring compared to other chapters. Students who have practiced previous year questions and basic numerical problems can solve these questions quickly within the limited time of the exam. Therefore, solving COMEDK-level practice questions with solutions is one of the best ways to master this chapter and maximize marks in the Mathematics section of COMEDK UGET 2026.

Also Check - COMEDK Chapter Wise PYQ for Mathematics

COMEDK UGET 2026 Matrices and Determinants Important Topics

While the Algebra section is one of the most scoring sections in the Mathematics paper, it is recommended that you prepare the Matrices and Determinants important topics to ensure you are able to solve all the questions with accuracy on the day of the exam. In the following table, we have provided the detailed Matrices and Determinants from the COMEDK 2026 syllabus:

Also Check - Do or Die Chapters for COMEDK UGET 2026 Mathematics

COMEDK UGET 2026 Matrices and Determinants Expected Weightage

COMEDK Matrices and Determinants weightage will help you understand how many marks will be covered from this chapter. As per recent trends, we can assume that Matrices weightage will be around 6-8%. Therefore, you can expect around 4-5 questions. In the following table, we have detailed the Matrices and Determinants weightage in COMEDK Mathematics exam:

COMEDK UGET 2026 Matrices and Determinants Practice Questions with Solutions

In this section, we have shared a few COMEDK UGET 2026 Matrices and Determinants practice questions with solutions. By attempting these mock questions, analyze your performance and track your progress. This will also help you to improve your speed and accuracy, and boost confidence before taking the actual exam.

Q1. If A (adj A) = 5I, where I is the identity matrix of order 3, then |adj A| =

a. 125

b. 25

c. 5

d. 10

Ans. b. 25

Solution: We start with the well-known property of matrices:

A.(adjA) = |A|.I

Where |A| denotes the determinant of A and I is the identity matrix.

In this problem, we are given:

A.(adjA) = 5I

Comparing the two equations, it follows directly that:

|A|I = 5I = 5

Next, recall another important property for any n x n matrix:

|adj A| = |A| ^n-1

Since A is of order 3 (n = 3), we have:

|adj A| = |A| ² = 25

Q2. A square matrix P satisfies P2 = I - P where I is the identity matrix. If Pn= 5I - 8P, then n is equal to?

a. 6

b. 4

c. 8

d. 10

Ans. a. 6

Solution: We start with the given relation for the square matrix P:

P ² = I - P

Since any power of P can be expressed in the form αI + βP, we write

P ⁿ = 5I - 8P

Let’s determine the coefficients step by step:

For n = 0

We have P ⁰ = I, so,

a ₀ = 1, b ₁ = 0,

For n = 1,

We have P ¹ = P

a ₁ = 0, and b ₁ = 1

For n = 2

a ₂ = 1, b ₂ = -1

For n =3, multiplying P ² .P

P ³ = 2P - I

a ₃ = -1, b ₃ = 2.

For n = 4, multiplying P ³ .P

P ⁴ = 2I - 3P

a ₄ = 2, b ₄ = -3

For n = 5, multiplying P ⁴ .P

P ⁵ = - 3I + 5P

a ₅ = -3, b ₅ = 5

For n = 6, multiplying P ⁵ .P

P ⁶ = 5I - 8P

a ₆ = 5, b ₆ = -8

Thus the correct answer is 6.

Q3. If A is a matrix of order 4 such that A(adj.A) = 10I, then |adj A| is equal to:

a. 10

b. 100

c. 1000

d. 10000

Ans. c. 1000

Solution: Given, A(adj A) = 10I

We know that A(adj.A) = |A|I

10I = |A|I

|A| = 10

We know that |adj A| = |A| ^n-1 , where n is order of A

10 ³ = 1000.

Q4. A and B are invertible matrices of the same order such that |(AB)-1| = 8 if |A| = 2 then |B| is:

a. 6

b. 16

c. 1\16

d. 4

Ans. c. 1/16

Solution: To solve this problem, we'll use the properties of determinants specifically relating to the multiplication of matrices and the determinant of an inverse matrix.

If A and B are invertible matrices of the same order, then

The determinant of the product of two matrices is the product of their determinants, i.e., |AB| = |A||B|

The determinant of the inverse of a matrix is the inverse of the determinant of the matrix, i.e., |(AB} ^-1 | = 1/|AB|

GIven, |(AB} ^-1 | = |AB| = 1/8

|AB| = |A||B|

|B| = 1/8 ∻ 2 = 1/16

Q5. Solution of x - y + z; x -2y +2z = 9 and 2x + y + 3z = 1 is:

a. x =3; y = 6; z = 9

b. x =-4; y = -3; z = 2

c. x = -1; y = -3; z = 2

d. x = 2; y = 4; z = 6

Ans. c. x = -1; y = -3; z = 2

Solution: To find the solution of the given system of linear equations:

x - y + z = 4 …1

x - 2y + 2z = 9 …2

2x + y +3z = 1 …3

Let's try to eliminate variables to solve for each variable and see which option fits:

First, subtract equation (1) from equation (2) to eliminate the variable x

(x - 2y + 2z) - (x - y + z) = 9 - 4 = 5

- y + z = 5 …(4)

Now, we can use equations (4) and (1) to eliminate z

Multiply equation (4) by -1 and add to equation (1):

z - y = -5

x - y + z = 4

x = -5 …(5)

From equation (4)

- y + z = 5

From equation 3

y = -3 …(6)

Simplifying,

z = 2 …(7)

x = -1; y = -3; z = 2

COMEDK UGET Matrices and Determinants Question Trends

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