Matrices and Determinants Most Repeated Questions for JEE Main 2026 | PYQ Quiz

Matrices and Determinants – Most Repeated Questions for JEE Main 2026

Matrices and Determinants is one of the most scoring chapters in JEE Main Mathematics. Almost every year 1–2 questions are asked from adjoint, inverse, determinant properties and consistency of linear equations.

This quiz contains most repeated PYQ-based questions asked previously in JEE Main. Practicing these questions will improve accuracy, speed and conceptual clarity for JEE Main 2026.

Q1. Let B = [[1,3],[1,5]] and A be a 2×2 matrix such that AB⁻¹ = A⁻¹. If BCB⁻¹ = A and C⁴ + αC² + βI = O, then the value of (2β − α) is:
16
10
8
2
📌 JEE Main 2022 (PYQ)
Correct Answer: 10
Using similarity transformation and Cayley–Hamilton theorem on matrix C.
Q2. Let P be a square matrix such that P² = I − P. If Pᵅ + Pᵝ = γI − 29P and Pᵅ − Pᵝ = δI − 13P, then α + β + γ − δ is:
18
22
24
40
📌 JEE Main PYQ Pattern
Correct Answer: 24
Higher powers of P reduce using relation P² = I − P.
Q3. If the system of equations has infinitely many solutions, then the value of (7a + 3b) is:
12
9
22
16
📌 JEE Main 2021
Correct Answer: 16
For infinite solutions, rank of coefficient matrix = rank of augmented matrix.
Q4. Let A satisfy Aⁿ = Aⁿ⁻² + A² − I. The sum of all elements of A⁵⁰ is:
44
39
52
53
📌 Repeated JEE Question Type
Correct Answer: 53
Using recurrence relation and cyclic nature of powers.
Q5. Let A = [[2,a,0],[1,3,1],[0,5,b]]. If A³ = 4A² − A − 21I, then the value of (2a + 3b) is:
−10
−12
−13
−9
📌 JEE Main PYQ
Correct Answer: −13
Using Cayley–Hamilton theorem on matrix A.
Q6. If det(A)=3 for a 3×3 matrix A, then det(adj(−4 adj(−3 adj(3 adj((2A)⁻¹))))) = 2ᵐ·3ⁿ. Find (m + 2n).
2
4
3
6
📌 Advanced JEE Pattern
Correct Answer: 4
Using det(adj(A)) = det(A)² and scalar properties.
Q7. If A = [[1,5],[λ,10]] and A⁻¹ = αA + βI with α + β = −2, then (4α² + β² + λ²) is:
12
10
19
14
📌 JEE Main PYQ
Correct Answer: 14
Comparing matrix coefficients after inversion.
Q8. Let det(A)=2. If adj is applied 2024 times on A, find remainder when determinant is divided by 9.
7
4
1
0
📌 JEE Main 2023 Type
Correct Answer: 7
Using adjoint determinant cycle for odd/even powers.
Q9. If a system has infinitely many solutions, then (μ − 2λ) is:
56
59
57
55
📌 JEE Main PYQ
Correct Answer: 57
Using rank consistency condition.
Q10. If det(adj(adj(3A))) = 2ᵐ·3ⁿ for det(A)=1, then (m + n) is:
22
20
24
26
📌 JEE Main PYQ
Correct Answer: 24
Using det(adj(adj(A))) = det(A)⁴.

Matrices and Determinants – JEE Main Theory

Important topics include adjoint, inverse, determinant properties, Cayley–Hamilton theorem and consistency of linear equations. Mastery of these ensures guaranteed marks in JEE Main.

FAQs – JEE Main 2026

Q. Are these questions enough for JEE Main?
Yes, these are most repeated PYQ-based questions.

Q. How many questions come from this chapter?
Usually 1–2 every year.

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