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Matrices

JEE Mains Maths. Try each one first, then open its answer.

Top 10 JEE Mains PYQs to practise first

The questions and kinds of question asked most often come first. Each one says how often and in which papers.

  1. Question 1

    This type asked 9 times: 2021 Paper 17, 29 Jun 2022, 25 Jul 2022, 12 Apr 2023, 4 Apr 2024, 29 Jan 2025, 21 Jan 2026 S2, 28 Jan 2026 S2, 6 Apr 2026 S2. This one: 6 Apr 2026 S2 See all 9 of this type

    55
    Let A=[100310931]A =\begin{bmatrix} 1 & 0 & 0 \\ 3 & 1 & 0 \\ 9 & 3 & 1 \end{bmatrix} and B=[bij],1≤i,j≤3B =\left\lbrack b_{ij} \right\rbrack,1 \leq i,j \leq 3. If B=A99−IB=A^{99}-I, then the value of b31−b21b32\frac{b_{31}-b_{21}}{b_{32}} is :

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  2. Question 2

    This type asked 6 times: 27 Jan 2024, 23 Jan 2025, 24 Jan 2025, 22 Jan 2026 S1, 5 Apr 2026 S1, 5 Apr 2026 S2. This one: 5 Apr 2026 S2 See all 6 of this type

    54
    Let M be a 3×33 \times 3 matrix such that M(100)=(123),M(010)=(012)M\begin{pmatrix} 1 \\ 0 \\ 0 \end{pmatrix}=\begin{pmatrix} 1 \\ 2 \\ 3 \end{pmatrix},M\begin{pmatrix} 0 \\ 1 \\ 0 \end{pmatrix}=\begin{pmatrix} 0 \\ 1 \\ 2 \end{pmatrix} and M(001)=(−111)M\begin{pmatrix} 0 \\ 0 \\ 1 \end{pmatrix}=\begin{pmatrix} - 1 \\ 1 \\ 1 \end{pmatrix}. If M(xyz)=(1711)M\begin{pmatrix} x \\ y \\ z \end{pmatrix}=\begin{pmatrix} 1 \\ 7 \\ 11 \end{pmatrix}, then x+y+zx + y + z equals :

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  3. Question 3

    This type asked 6 times: 27 Jun 2022, 31 Jan 2023, 10 Apr 2023, 22 Jan 2025, 23 Jan 2026 S1, 24 Jan 2026 S2. This one: 24 Jan 2026 S2 See all 6 of this type

    58
    Let P=[pij]P =\left\lbrack p_{ij} \right\rbrack and Q=[qij]Q =\left\lbrack q_{ij} \right\rbrack be two square matrices of order 3 such that qij=2(i+j−1)pijq_{ij}=2^{(i + j - 1)}p_{ij} and det(Q)=210det(Q) =2^{10}. Then the value of det(adj(adjP))det(adj(adjP)) is :

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  4. Question 4

    This type asked 5 times: 2021 Paper 10, 29 Jan 2023, 6 Apr 2023, 2 Apr 2025, 4 Apr 2025. This one: 4 Apr 2025 See all 5 of this type

    136
    Let the matrix A=[100101010]A=\begin{bmatrix} 1 & 0 & 0 \\ 1 & 0 & 1 \\ 0 & 1 & 0 \end{bmatrix} satisfy An=An−2+A2−A^{n}=A^{n- 2}+A^{2}- I for n≥3n \geq 3. Then the sum of all the elements of A50A^{50} is :-

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  5. Question 5

    This type asked 4 times: 29 Jun 2022, 31 Jan 2023, 29 Jan 2025, 2 Apr 2025. This one: 2 Apr 2025 See all 4 of this type

    55
    Let A=[α−16β],α>0A=\begin{bmatrix} \alpha & - 1 \\ 6 & \beta \end{bmatrix},\alpha> 0, such that det(A)=0det(A) = 0 and α+β=1\alpha+\beta= 1. If I denotes 2×22 \times 2 identity matrix, then the matrix (1+A)8(1 +A)^{8} is:

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  6. Question 6

    This type asked 4 times: 2021 Paper 18, 25 Jan 2023, 8 Apr 2023, 28 Jan 2025. This one: 28 Jan 2025 See all 4 of this type

    135
    Let A=[12−201]A =\begin{bmatrix} \frac{1}{\sqrt{2}} & - 2 \\ 0 & 1 \end{bmatrix} and P=[cos⁡θ−sin⁡θsin⁡θcos⁡θ],θ>0P =\begin{bmatrix} \cos\theta & - \sin\theta \\ \sin\theta & \cos\theta \end{bmatrix},\theta > 0. If B=PAPT,C=PTB10PB = PAP^{T},C =P^{T}B^{10}P and the sum of the diagonal elements of C is mn\frac{m}{n}, where gcd(m,n)=gcd(m,n) = 1 , then m+nm + n is :

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  7. Question 7

    This type asked 4 times: 2021 Paper 16, 27 Jul 2022, 8 Apr 2023, 4 Apr 2024. This one: 4 Apr 2024 See all 4 of this type

    175
    Let A be a 2×22 \times 2 symmetric matrix such that A[11]=[37]A\begin{bmatrix} 1 \\ 1 \end{bmatrix}=\begin{bmatrix} 3 \\ 7 \end{bmatrix} and the determinant of AA be 1. If A−1=αA+βIA^{- 1}= \alpha A + \beta I, where II is an identity matrix of order 2×22 \times 2, then α+β\alpha + \beta equals....

  8. Question 8

    This type asked 3 times: 2021 Paper 23, 26 Jul 2022, 4 Apr 2026 S1. This one: 4 Apr 2026 S1 See all 3 of this type

    55
    Let S={A=[abcd]:a,b,c,d∈{0,1,2,3,4}S =\left\{ A =\begin{bmatrix} a & b \\ c & d \end{bmatrix}\mathbf{:a,b,c,d \in \{ 0,1,2,3,4\}} \right. and  A2−4 A+3I=0}\left. \ A^{2}- 4\text{ }A + 3I = 0 \right\} be a set of 2×22 \times 2 matrices. Then the number of matrices in S, for which the sum of the diagonal elements is equal to 4 , is:

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  9. Question 9

    This type asked 3 times: 2021 Paper 2, 28 Jul 2022, 25 Jan 2023. This one: 25 Jan 2023 See all 3 of this type

    167
    Let A, B, C be 3×33 \times 3 matrices such that AA is symmetric and BB and CC are skew-symmetric. Consider the statements (S1) A13 B26−B26 A13A^{13}{\text{ }B}^{26}-B^{26}{\text{ }A}^{13} is symmetric (S2) A26C13−C13 A26A^{26}C^{13}-C^{13}{\text{ }A}^{26} is symmetric Then,

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  10. Question 10

    This type asked 3 times: 2021 Paper 14, 28 Jun 2022, 25 Jul 2022. This one: 25 Jul 2022 See all 3 of this type

    81
    Let A=[2−1−110−11−10]A =\begin{bmatrix} 2 & - 1 & - 1 \\ 1 & 0 & - 1 \\ 1 & - 1 & 0 \end{bmatrix} and B=A−IB = A - I. If ω=3i−12\omega =\frac{\sqrt{3}i - 1}{2}, then the number of elements in the set {n∈{1,2,…,100}:An+(ωB)n=A+B}\left\{ \mathbf{n \in \{ 1,2,\ldots,100\}:}A^{n}+ (\omega B)^{n}= A + B \right\} is equal to