PrepWiser › Learn › Mathematics › MatricesMatrices — JEE Main PYQs & Practice Questions Matrices is a Mathematics chapter in the JEE Main syllabus. This page brings together 118 previous-year and practice questions on Matrices, organised into 4 topics: Types of Matrices and Operations, Transpose, Symmetric and Skew-Symmetric, Orthogonal Matrix and Inverse of a Matrix. Most questions come with a step-by-step solution you can work through free in PrepWiser.
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Types of Matrices and Operations Let A=[0, 1, 2; a, 0, 3; 1, c, 0], where a, c ∈ ℝ. If A³=A and the positive value of a… Let X=[1; 1; 1] and A=[-1, 2, 3; 0, 1, 6; 0, 0, -1]. For k ∈ N, if X′ Aᵏ X=33, then k is… The total number of 3 × 3 matrices A having entries from the set 0, 1, 2, 3 such that… Let A=[1, 2; 1, α] and B=[3, 3; β, 2]. If A²-4A+I=O and B²-5B-6I=O, then among the two… Let A = [ x, 1; 1, 0 ], x ∈ R and A⁴ = [aᵢⱼ]. If a₁₁ = 109, then a₂₂ is equal to _______ . Let A=[α, -1; 6, β], α>0, such that det(A)=0 and α+β=1. If I denotes 2 × 2 identity… Let A = ( 1, - 1, 0; 0, 1, - 1; 0, 0, 1 ) and B = 7A²⁰ - 20A⁷ + 2I, where I is an… For some α,β∈ R, let A=[α, 2; 1, 2] and B=[1, 1; 1, β] be such that A²-4A+2I=B²-3B+I=O… Let A = ( 2, - 2; 1, - 1 ) and B = ( - 1, 2; - 1, 2 ). Then the number of elements in… Let A = [ 0, 1, 0; 1, 0, 0; 0, 0, 1 ]. Then the number of 3 × 3 matrices B with entries… Let A be a 2 × 2 real matrix with entries from 0, 1 and |A| ≠ 0. Consider the following… Let A=[2, a, 0; 1, 3, 1; 0, 5, b]. If A³=4 A²-A-21 I, where I is the identity matrix of… Let I be an identity matrix of order 2 × 2 and P = [ 2, - 1; 5, - 3 ]. Then the value of… Let A = [aᵢⱼ] be a real matrix of order 3 × 3, such that aᵢ₁ + aᵢ₂ + aᵢ₃ = 1, for i = 1… Let A and B be two 3 × 3 non-zero real matrices such that AB is a zero matrix. Then Let A = [ 0, - 2; 2, 0 ]. If M and N are two matrices given by M = Σₖ₌₁¹⁰ A²ᵏ and N =… If the matrix A = ( 0, 2; K, - 1 ) satisfies A(A³ + 3I) = 2I, then the value of K is : If P = [ 1, 0; 1/2, 1 ], then P⁵⁰ is : If A = [ 1, 1, 1; 0, 1, 1; 0, 0, 1 ] and M = A + A² + A³ + ....... + A²⁰, then the sum… Let A be a 3 × 3 matrix having entries from the set -1, 0, 1. The number of all such… Transpose, Symmetric and Skew-Symmetric Let A, B, C be 3 × 3 matrices such that A is symmetric and B and C are skew-symmetric… Let A be a square matrix such that AAᵀ=I. Then 1/2 A[(A+Aᵀ)²+(A-Aᵀ)²] is equal to Let A = [ 2, 3; a, 0 ], a∈R be written as P + Q where P is a symmetric matrix and Q is… Let A and B be any two 3 × 3 symmetric and skew symmetric matrices respectively. Then… If A = [1 2; 3 4], then A + Aᵀ is: Let A be a 2 × 2 matrix with real entries such that A'=α A+I, where α ∈ ℝ-{-1,1}. If… If P is a 3 × 3 real matrix such that Pᵀ=a P+(a-1) I, where a>1, then : Let A be a symmetric matrix of order 2 with integer entries. If the sum of the diagonal… The number of symmetric matrices of order 3, with all the entries from the set… Let A=[1; 1; 1] and B=[9², -10², 11²; 12², 13², -14²; -15², 16², 17²] , then the value… Let S be the set containing all 3 × 3 matrices with entries from {-1,0,1}. The total… Let M denote the set of all real matrices of order 3 × 3 and let S={-3,-2,-1,1,2}. Let… Orthogonal Matrix Let P=[√3/2, 1/2; -1/2, √3/2], A=[1, 1; 0, 1] and Q=P A Pᵀ. If Pᵀ Q²⁰⁰⁷ P=[a, b; c, d]… If for the matrix, A = [ 1, - α; α, β ], AAᵀ = I₂, then the value of α ⁴ + β ⁴ is : If A = 1/2[ 1, √3; - √3, 1 ], then : Let α be a root of the equation x² + x + 1 = 0 and the matrix A = 1/√3[ 1, 1, 1; 1, α, α… Let A=[1/√2, -2; 0, 1] and P=[cos θ, -sin θ; sin θ, cos θ], θ>0. If B=PAP ᵀ, C=Pᵀ B¹⁰ P… Let A=I₂-2 M Mᵀ, where M is a real matrix of order 2 × 1 such that the relation Mᵀ M=I₁… Let A = [ a₁; a₂ ] and B = [ b₁; b₂ ] be two 2 × 1 matrices with real entries such that… Let a, b, c ∈ R be all non-zero and satisfy a³ + b³ + c³ = 2. If the matrix A = ( a, b… Inverse of a Matrix Let R=(x, 0, 0; 0, y, 0; 0, 0, z) be a non-zero 3 × 3 matrix, where x sin θ=y sin (θ+(2… Consider the matrices A=[2, -2; 4, -2] and B=[3, 9; 1, 3]. If matrices P and Q are such… Let A=(1, 2; -2, -5). Let α, β ∈ ℝ be such that α A²+β A=2 I. Then α+β is equal to If A=[1, 5; λ, 10], A⁻¹=α A+β I and α+β=-2, then 4 α²+β²+λ² is equal to : If A, B, and(adj(A⁻¹)+adj(B⁻¹)) are non-singular matrices of same order, then the… If A is invertible, then A⁻¹ = (AB)⁻¹ = B⁻¹ A⁻¹ for all invertible matrices A and B. Let A = ( 2, - 1; 0, 2 ). If B = I - ⁵C₁(adj A) + ⁵C₂(adj A)² - ..... - ⁵C₅(adj A)⁵… Let X = [ 0, 1, 0; 0, 0, 1; 0, 0, 0 ], Y = α I + β X + γ X² and Z = α ²I - α β X + (β ²… Let A = [ 1/√10, 3/√10; (- 3)/√10, 1/√10 ] and B = [ 1, - i; 0, 1 ], where i = √(- 1)… Let for A = [ 1, 2, 3; α, 3, 1; 1, 1, 2 ],|A| = 2. If |2 adj (2 adj (2A))| = 32ⁿ, then… Let A=(m, n; p, q), d=|A| ≠ 0 and |A-d(A d j A)|=0. Then Let A,B and C be three 2× 2 matrices with real entries such that B=(I+A)⁻¹ and A+C=I. If… Let A = [ 1, 2; - 1, 4 ]. If A⁻¹ = αI + βA, α, β ∈ R, I is a 2 × 2 identity matrix then… If A = ( 1/√5, 2/√5; (- 2)/√5, 1/√5 ), B = ( 1, 0; i, 1 ), i = √(- 1), and Q = A T BA… Let A = [aᵢⱼ] be a square matrix of order 3 such that aᵢⱼ = 2ʲ⁻ⁱ, for all i, j = 1, 2… Let A be a n × n matrix such that |A|=2. If the determinant of the matrix Adj(2 · Adj(2… Let A=[1, 2; 0, 1] and B=I+adj(A)+(adj A)²+…+(adj A)¹⁰. Then, the sum of all the… Let A=[2, 0, 1; 1, 1, 0; 1, 0, 1], B=[B₁, B₂, B₃], where B₁, B₂, B₃ are column matrics… Consider the matrix f(x)=[cos x, -sin x, 0; sin x, cos x, 0; 0, 0, 1]. Given below are… More Mathematics chapters Frequently asked questions How many Matrices questions are there for JEE Main? PrepWiser has 118 Matrices questions for JEE Main, grouped into 4 topics such as Types of Matrices and Operations, Transpose, Symmetric and Skew-Symmetric and Orthogonal Matrix.
Are these Matrices questions from previous-year JEE Main papers? Yes — most are genuine previous-year questions from past JEE Main papers, and the rest are practice questions written to match the JEE Main pattern and difficulty.
Where can I see the answers and solutions to these Matrices questions? Open any Matrices question in PrepWiser (it is free) to attempt it; most come with a step-by-step solution.