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Saturday, 31 October

JEE Main · Maths · Matrices

Powers of Square Matrices

JEE Main asked Powers of Square Matrices 21 times in 21 of the 108 shifts Lumi analysed, in 2020, 2021, 2022, 2023, 2024 and 2025. It belongs to Matrix Multiplication, in Matrices (Maths). The longest wait between two years asking it was 1 year. In 2020, 2021, 2022, 2023 and 2024 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
21
in 21 shifts
Years
6 of 8
First asked
2020
last in 2025
Pattern
Asked most years
across the analysed shifts

Questions on this idea a shift, by year

2017–2026. Asked in 2020, 2021, 2022, 2023, 2024 and 2025. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.150.30’170.17’200.24’210.18’220.28’230.09’240.13’250’26

Raw count: 2017: 0 in 1 shift · 2020: 2 in 12 shifts · 2021: 7 in 24 shifts · 2022: 5 in 24 shifts · 2023: 4 in 12 shifts · 2024: 2 in 18 shifts · 2025: 1 in 8 shifts · 2026: 0 in 9 shifts.

Shift by shift

Each square is one analysed shift, in date order. Open a filled one for that paper.

  • 20260 of 9
  • 20251 of 8
  • 20242 of 18
  • 20234 of 12
  • 20225 of 24
  • 20217 of 24
  • 20202 of 12
  • 20170 of 1

Asked in that shift More than once Not asked

How JEE Main framed it

Single correct is the usual form. Skill tested: multi-step.

  • Sum of elements of high matrix power from recurrence
  • Power of upper triangular matrix

Difficulty

Easy 1Medium 12Hard 8

10 of the 21 questions had a numerical answer.

Every question

All 21 questions

From the official JEE Main shift papers, newest first. Open one for the full question, the options and the official answer.

  1. 4 Apr 2025, Shift 2 · Q4Let the matrix A=[100101010]A=\begin{bmatrix}1&0&0\\1&0&1\\0&1&0\end{bmatrix} satisfy An=An−2+A2−IA^n=A^{n-2}+A^2-I for n≥3n\ge 3. Then the sum of all the…HardSingle correct
  2. 8 Apr 2024, Shift 1 · Q22Let A=[2−111]A=\begin{bmatrix}2&-1\\1&1\end{bmatrix}. If the sum of the diagonal elements of A13A^{13} is 3n3^n, then nn is equal to ____________.MediumNumerical value
  3. 4 Apr 2024, Shift 2 · Q3Let A=[1201]A=\begin{bmatrix}1&2\\0&1\end{bmatrix} and B=I+adj(A)+(adj A)2+…+(adj A)10B=I+\mathrm{adj}(A)+(\mathrm{adj}\,A)^2+\ldots+(\mathrm{adj}\,A)^{10}. Then, the sum of…MediumSingle correct
  4. 12 Apr 2023, Shift 1 · Q3Let A=[115101]A=\begin{bmatrix}1&\frac{1}{51}\\0&1\end{bmatrix}. If…HardSingle correct
  5. 11 Apr 2023, Shift 1 · Q29Let A=[012a031c0]A = \begin{bmatrix} 0 & 1 & 2 \\ a & 0 & 3 \\ 1 & c & 0 \end{bmatrix}, where a,c∈Ra, c \in \mathbb{R}. If A3=AA^3 = A and the positive…HardNumerical value
  6. 8 Apr 2023, Shift 1 · Q5Let P=[3212−1232]P=\begin{bmatrix}\frac{\sqrt{3}}{2}&\frac{1}{2}\\-\frac{1}{2}&\frac{\sqrt{3}}{2}\end{bmatrix},…HardSingle correct
  7. 6 Apr 2023, Shift 2 · Q4Let PP be a square matrix such that P2=I−PP^2=I-P. For α,β,γ,δ∈N\alpha,\beta,\gamma,\delta\in\mathbb{N}, if Pα+Pβ=γI−29PP^\alpha+P^\beta=\gamma I-29P and…HardSingle correct
  8. 29 Jun 2022, Shift 1 · Q10Let A=[aij]A = [a_{ij}] be a square matrix of order 3 such that aij=2j−ia_{ij} = 2^{j-i}, for all i,j=1,2,3i, j = 1, 2, 3. Then, the matrix…MediumSingle correct
  9. 24 Jun 2022, Shift 2 · Q22Let S={(−1a0b):a,b∈{1,2,3,…100}}S = \left\{\begin{pmatrix} -1 & a \\ 0 & b \end{pmatrix} : a, b \in \{1, 2, 3, \ldots 100\}\right\} and let…HardNumerical value
  10. 29 Jul 2022, Shift 2 · Q23Let X=[111]X=\begin{bmatrix}1\\1\\1\end{bmatrix} and A=[−12301600−1]A=\begin{bmatrix}-1 & 2 & 3\\ 0 & 1 & 6\\ 0 & 0 & -1\end{bmatrix}. For k∈Nk\in\mathbb{N},…MediumNumerical value
  11. 25 Jul 2022, Shift 2 · Q23Let A=[1aa01b001]A=\begin{bmatrix}1&a&a\\0&1&b\\0&0&1\end{bmatrix}, a,b∈Ra,b\in\mathbb{R}. If for some n∈Nn\in\mathbb{N},…MediumNumerical value
  12. 25 Jul 2022, Shift 1 · Q21Let A=(2−1−110−11−10)A=\begin{pmatrix}2&-1&-1\\1&0&-1\\1&-1&0\end{pmatrix} and B=A−IB=A-I. If ω=3 i−12\omega=\frac{\sqrt3\,i-1}{2}, then the number of elements in…HardNumerical value
  13. 25 Jul 2021, Shift 2 · Q75If P=[10121]P=\begin{bmatrix}1&0\\ \frac{1}{2}&1\end{bmatrix}, then P50P^{50} is :EasySingle correct
  14. 25 Jul 2021, Shift 1 · Q87Let…MediumNumerical value
  15. 22 Jul 2021, Shift 2 · Q64Let A=[aij]\mathrm{A}=[\mathrm{a}_{ij}] be a real matrix of order 3×33\times3, such that ai1+ai2+ai3=1\mathrm{a}_{i1}+\mathrm{a}_{i2}+\mathrm{a}_{i3}=1,…MediumSingle correct
  16. 25 Feb 2021, Shift 1 · Q82Let A=[xyzyzxzxy]\mathrm{A} = \begin{bmatrix} x & y & z \\ y & z & x \\ z & x & y \end{bmatrix}, where xx, yy and zz are real numbers such that…HardNumerical value
  17. 26 Aug 2021, Shift 2 · Q64Let A=(100011100)\mathrm{A}=\begin{pmatrix}1&0&0\\0&1&1\\1&0&0\end{pmatrix}. Then A2025−A2020\mathrm{A}^{2025}-\mathrm{A}^{2020} is equal to :MediumSingle correct
  18. 4 Aug 2021, Shift 2 · Q83If A=[100110111]A=\begin{bmatrix}1&0&0\\1&1&0\\1&1&1\end{bmatrix}, the sum of the entries of A20A^{20} is ________ .MediumNumerical value
  19. 3 Aug 2021, Shift 1 · Q62Let A=(010001100)A = \begin{pmatrix} 0 & 1 & 0 \\ 0 & 0 & 1 \\ 1 & 0 & 0 \end{pmatrix} and…MediumSingle correct
  20. 4 Sep 2020, Shift 1 · Q54If A =[cos⁡θisin⁡θisin⁡θcos⁡θ]= \begin{bmatrix} \cos\theta & i\sin\theta \\ i\sin\theta & \cos\theta \end{bmatrix}, (θ=π24)\left(\theta = \frac{\pi}{24}\right) and…MediumSingle correct
  21. 3 Sep 2020, Shift 1 · Q72Let A=[x110]A=\begin{bmatrix}x&1\\1&0\end{bmatrix}, x∈Rx\in\mathbf{R} and A4=[aij]A^4=[a_{ij}]. If a11=109a_{11}=109, then a22a_{22} is equal to __________.MediumNumerical value

Shifts: 3 Sep 2020, Shift 1, 4 Sep 2020, Shift 1, 25 Feb 2021, Shift 1, 22 Jul 2021, Shift 2, 25 Jul 2021, Shift 2, 25 Jul 2021, Shift 1, 3 Aug 2021, Shift 1, 4 Aug 2021, Shift 2, 26 Aug 2021, Shift 2, 24 Jun 2022, Shift 2, 29 Jun 2022, Shift 1, 25 Jul 2022, Shift 2, 25 Jul 2022, Shift 1, 29 Jul 2022, Shift 2, 6 Apr 2023, Shift 2, 8 Apr 2023, Shift 1, 11 Apr 2023, Shift 1, 12 Apr 2023, Shift 1, 4 Apr 2024, Shift 2, 8 Apr 2024, Shift 1, 4 Apr 2025, Shift 2.

Same topic

Other ideas in Matrix Multiplication

Matrix Multiplication has 19 ideas JEE Main has asked; 8 of them came up in more than one question. The 12 most asked are below.

Topic analysisChapter analysisStudy this chapterAll repeated ideas