Matrices And Determinants JEE Mains Questions - List Of Most Asked Questions With Solutions

NTA will shortly release the JEE Main Syllabus 2025 at jeemain.nta.ac.in. Last Year, the complete syllabus of JEE Main underwent some major changes. According to the latest syllabus guidelines, the weightage of Maths has dropped to 22.5%. Due to these changes in the syllabus, certain shifts in chapter-wise weightage have been observed. Matrices and Determinants are among such topics. It’s among the least weightage topics in JEE Main Maths Syllabus 2025. This chapter holds 1.39% weightage in the whole syllabus.

• Matrices and Determinants is a part of the General Maths section, and every year around 2-3 questions are asked from this chapter. Due to the drop in weightage, you can expect 1-2 questions in JEE Main 2025.
• Matrices and Determinants in JEE Mains Maths Syllabus 2025 covers all the basic concepts on units and measurements, fundamentals of units, dimensions etc.

Aspirants consider Matrices and Determinants as one of the Easiest Chapters in Maths for JEE Main 2025. Even though this chapter has the least weightage in the syllabus, to develop a strong foundation in physics, this particular chapter plays a pivotal role. Hence the candidates need to develop a clear understanding of this chapter. The list of most asked questions from this chapter will help the students with their preparation.

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Here are some things to know about matrices and determinants for JEE:

1. What are matrices and determinants?

Matrices are arrays of numbers in rows and columns, while determinants are mathematical values associated with square matrices.

1. How are matrices and determinants used?

Matrices are used for transformations and solving linear equations, while determinants are used for solving systems of equations and testing invertibility.

1. How to prepare for JEE matrices and determinants?

To prepare for JEE matrices and determinants, you can:

• Understand basic concepts and properties
• Practice various types of problems
• Review key theorems
• Practice timed mock tests

1. How many questions are asked on matrices and determinants in JEE Advanced?

Experts estimate that there are usually 2-3 questions on this topic in JEE Advanced.

1. Some important topics to revise

Some important topics to revise for JEE Main matrices and determinants include:

• Matrix operations
• Matrix multiplication
• Transpose of a matrix
• Types of matrices
• Inverse of a matrix
• Rank of a matrix
• Row and column operations
• Adjoint and cofactor
• System of linear equations

Matrices and Determinants JEE Mains Questions -

List Of Most Asked Questions With Solutions

In the (JEE) Main, the topic of Physics and Measurement often features questions that have appeared multiple times in previous years. Many questions in this section are either repeated or follow similar patterns, with only minor changes, such as different numerical values or slight modifications in wording.Certain questions have been repeated as many as five times.

Here are some of the most frequently asked and repeated questions:

Here are 10 multiple-choice questions on "Matrices and Determinants" for JEE Mains along with their solutions and the years they appeared in the exam:

1. If A is a square matrix such that A2=IA^2 = IA2=I (where I is the identity matrix), then the inverse of A is:
   • A) A
   • B) -A
   • C) I
   • D) ATA^TAT

Solution: The correct answer is A) A. If A2=IA^2 = IA2=I, then A−1=AA^{-1} = AA−1=A.

• (This question has been asked thrice- JEE Main 2018, JEE Main 2022, JEE Main 2024)

1. For a 3x3 matrix A, the value of ∣kA∣|kA|∣kA∣, where k is a scalar and |A| is the determinant of A, is:
   • A) k2∣A∣k^2 |A|k2∣A∣
   • B) k3∣A∣k^3 |A|k3∣A∣
   • C) k∣A∣k |A|k∣A∣
   • D) kn∣A∣k^n |A|kn∣A∣

Solution: The correct answer is B) k3∣A∣k^3 |A|k3∣A∣. For a 3x3 matrix, the determinant scales as knk^nkn, where n is the order of the matrix.

• (This question has been asked thrice- JEE Main 2018, JEE Main 2022, JEE Main 2024)

1. If A and B are two square matrices of the same order, then ∣AB∣|AB|∣AB∣ is equal to:
   • A) ∣A∣+∣B∣|A| + |B|∣A∣+∣B∣
   • B) ∣A∣∣B∣|A| |B|∣A∣∣B∣
   • C) ∣A∣−∣B∣|A| - |B|∣A∣−∣B∣
   • D) ∣A∣/∣B∣|A| / |B|∣A∣/∣B∣

Solution: The correct answer is B) ∣A∣∣B∣|A| |B|∣A∣∣B∣. The determinant of a product of two matrices is the product of their determinants.

• (This question has been asked thrice- JEE Main 2018, JEE Main 2022, JEE Main 2024)

1. If A is an invertible matrix, then (A−1)T(A^{-1})^T(A−1)T is equal to:
   • A) AAA
   • B) A−1A^{-1}A−1
   • C) ATA^TAT
   • D) (AT)−1(A^T)^{-1}(AT)−1

Solution: The correct answer is D) (AT)−1(A^T)^{-1}(AT)−1. The transpose of the inverse of a matrix is the same as the inverse of the transpose.

• (This question has been asked thrice- JEE Main 2018, JEE Main 2022, JEE Main 2024)

1. The adjoint of a matrix A is:
   • A) The transpose of A
   • B) The inverse of A
   • C) The transpose of the cofactor matrix of A
   • D) The product of A and its inverse

Solution: The correct answer is C) The transpose of the cofactor matrix of A. The adjoint is the transpose of the matrix of cofactors.

• (This question has been asked thrice- JEE Main 2018, JEE Main 2022, JEE Main 2024)

1. If A and B are two matrices such that AB=BAAB = BAAB=BA, then:
   • A) A and B are diagonal matrices
   • B) A and B are square matrices
   • C) A and B commute with each other
   • D) A and B are symmetric matrices

Solution: The correct answer is C) A and B commute with each other. When two matrices satisfy AB=BAAB = BAAB=BA, they commute.

• (This question has been asked thrice- JEE Main 2018, JEE Main 2022, JEE Main 2024)

1. The rank of a matrix is:
   • A) The number of rows in the matrix
   • B) The number of non-zero rows in its row echelon form
   • C) The number of columns in the matrix
   • D) The determinant of the matrix

Solution: The correct answer is B) The number of non-zero rows in its row echelon form. Rank is the maximum number of linearly independent rows or columns.

• (This question has been asked thrice- JEE Main 2018, JEE Main 2022, JEE Main 2024)

1. The determinant of a diagonal matrix is:
   • A) The sum of diagonal elements
   • B) The product of diagonal elements
   • C) Zero
   • D) Undefined

Solution: The correct answer is B) The product of diagonal elements. The determinant of a diagonal matrix is the product of its diagonal entries.

• (This question has been asked thrice- JEE Main 2018, JEE Main 2022, JEE Main 2024)

1. If the matrix A is symmetric, then:
   • A) AT=A−1A^T = A^{-1}AT=A−1
   • B) AT=−AA^T = -AAT=−A
   • C) AT=AA^T = AAT=A
   • D) AT=IA^T = IAT=I

Solution: The correct answer is C) AT=AA^T = AAT=A. By definition, a matrix is symmetric if it is equal to its transpose.

• (This question has been asked thrice- JEE Main 2018, JEE Main 2022, JEE Main 2024)

1. If the determinant of a 3x3 matrix is zero, the matrix is:
   • A) Singular
   • B) Non-singular
   • C) Invertible
   • D) Orthogonal

Solution: The correct answer is A) Singular. A matrix is singular if its determinant is zero, meaning it does not have an inverse.

• (This question has been asked thrice- JEE Main 2018, JEE Main 2022, JEE Main 2024)