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Friday, 9 October

JEE Main Maths · Class 12

Matrices: JEE Main previous year questions

Matrices had 28 questions in the 42 JEE Main shifts Lumi analysed, about 0.6 a shift, asked in 24 of 42 shifts. It ranks 19 of 22 Maths chapters by questions; 25% of its questions were hard.

Questions
28
in 24 of 42 shifts
A shift, on average
0.6
of 25 Maths questions
Since 2024
+0.1
0.5 a shift in 2017–23, 0.6 in 2024–26
Numerical answer
9
32% of its questions

Year by year

How often it came

Questions in the analysed shifts of each year. Years differ in how many shifts Lumi analysed, so read the bars with the shift count.

Questions each year
0360’172’203’213’224’234’246’256’26

2017: 1 shifts · 2020: 4 shifts · 2021: 4 shifts · 2022: 4 shifts · 2023: 4 shifts · 2024: 8 shifts · 2025: 8 shifts · 2026: 9 shifts

Difficulty by year
  • 2017
  • 20202
  • 20213
  • 20223
  • 20234
  • 20244
  • 20256
  • 20266
  • Easy
  • Medium
  • Hard

Inside the chapter

Topics and the ideas that repeat

4 topics and 14 distinct ideas; 3 ideas were asked more than once. Most questions are single correct and multi-step.

Topics, by questions

2 questions had no close topic in our taxonomy and are counted for the chapter only.

Ideas asked most
3 repeat

Study it on Lumi

Matrices: the interactive lesson

Every question

All 28 Matrices questions

Newest first. Each opens with its options and the official answer.

2026 6 questions

  1. 2 Apr 2026, Shift 1 · Q4Let A=[121α]A=\begin{bmatrix}1&2\\1&\alpha\end{bmatrix} and B=[33β2]B=\begin{bmatrix}3&3\\\beta&2\end{bmatrix}. If A2−4A+I=OA^2-4A+I=O and B2−5B−6I=OB^2-5B-6I=O,…HardOther
  2. 2 Apr 2026, Shift 2 · Q3If the system of equations x+5y+6z=4,x + 5y + 6z = 4, 2x+3y+4z=7,2x + 3y + 4z = 7, x+6y+az=bx + 6y + az = b has infinitely many solutions, then the point (a,b)(a, b)…MediumSingle correct
  3. 2 Apr 2026, Shift 2 · Q22Consider the matrices A=[2−24−2]A = \begin{bmatrix} 2 & -2 \\ 4 & -2 \end{bmatrix} and B=[−3913]B = \begin{bmatrix} -3 & 9 \\ 1 & 3 \end{bmatrix}. If…MediumNumerical value
  4. 4 Apr 2026, Shift 1 · Q5Let S={A=[abcd]:a,b,c,d∈{0,1,2,3,4} and A2−4A+3I=0}S=\left\{A=\begin{bmatrix}a&b\\c&d\end{bmatrix}: a,b,c,d\in\{0,1,2,3,4\}\text{ and }A^2-4A+3I=0\right\} be a set of 2×22\times2…HardSingle correct
  5. 5 Apr 2026, Shift 2 · Q4Let M be a 3×33\times 3 matrix such that M(100)=(123)M\begin{pmatrix}1\\0\\0\end{pmatrix}=\begin{pmatrix}1\\2\\3\end{pmatrix},…MediumSingle correct
  6. 6 Apr 2026, Shift 2 · Q5Let A=[100310931]A=\begin{bmatrix}1&0&0\\3&1&0\\9&3&1\end{bmatrix} and B=[bij]B=[b_{ij}], 1≤i,j≤31\le i,j\le 3. If B=A99−IB=A^{99}-I, then the value of…MediumSingle correct

2025 6 questions

  1. 2 Apr 2025, Shift 1 · Q18Let A=[α−16β]A=\begin{bmatrix}\alpha&-1\\6&\beta\end{bmatrix}, α>0\alpha>0, such that det⁡(A)=0\det(A)=0 and α+β=1\alpha+\beta=1. If I denotes 2×22\times2…MediumSingle correct
  2. 2 Apr 2025, Shift 2 · Q3Let AA be a 3×33\times3 real matrix such that A2(A−2I)−4(A−I)=OA^2(A-2I) - 4(A-I) = O, where II and OO are the identity and null matrices,…MediumSingle correct
  3. 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
  4. 7 Apr 2025, Shift 1 · Q5Let AA be a 3×33 \times 3 matrix such that ∣adj(adj(adj A))∣=81|\mathrm{adj}(\mathrm{adj}(\mathrm{adj}\,A))| = 81. If…HardSingle correct
  5. 7 Apr 2025, Shift 1 · Q22The number of singular matrices of order 2, whose elements are from the set {2,3,6,9}\{2, 3, 6, 9\}, is ___________.MediumNumerical value
  6. 8 Apr 2025, Shift 2 · Q5Let α\alpha be a solution of x2+x+1=0x^2 + x + 1 = 0, and for some aa and bb in R\mathbb{R},…MediumSingle correct

2024 4 questions

  1. 8 Apr 2024, Shift 1 · Q4Let A=[2a013105b]A=\begin{bmatrix}2&a&0\\1&3&1\\0&5&b\end{bmatrix}. If A3=4A2−A−21IA^3=4A^2-A-21I, where II is the identity matrix of order 3×33\times3, then…MediumSingle 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. 9 Apr 2024, Shift 2 · Q4Let B=[1315]B=\begin{bmatrix}1&3\\1&5\end{bmatrix} and AA be a 2×22\times2 matrix such that AB−1=A−1AB^{-1}=A^{-1}. If BCB−1=ABCB^{-1}=A and…HardSingle correct
  4. 29 Jan 2024, Shift 1 · Q4Let A be a square matrix such that AAT=IAA^T=I. Then 12A[(A+AT)2+(A−AT)2]\frac{1}{2}A\left[(A+A^T)^2+(A-A^T)^2\right] is equal toMediumSingle correct

2023 4 questions

  1. 6 Apr 2023, Shift 1 · Q3Let A=[aij]2×2A=[a_{ij}]_{2\times2}, where aij≠0a_{ij}\neq0 for all i, j and A2=IA^2=I. Let aa be the sum of all diagonal elements of AA and b=∣A∣b=|A|.…MediumSingle correct
  2. 8 Apr 2023, Shift 2 · Q4If A=[15λ10]A = \begin{bmatrix} 1 & 5 \\ \lambda & 10 \end{bmatrix}, A−1=αA+βIA^{-1} = \alpha A + \beta I and α+β=−2\alpha + \beta = -2, then…MediumSingle correct
  3. 11 Apr 2023, Shift 1 · Q6Let AA be a 2×22 \times 2 matrix with real entries such that A′=αA+IA' = \alpha A + I, where α∈R−{−1,1}\alpha \in \mathbb{R} - \{-1, 1\}. If…MediumSingle correct
  4. 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

2022 3 questions

  1. 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
  2. 28 Jul 2022, Shift 1 · Q25Let A=[1−12α]A=\begin{bmatrix}1&-1\\2&\alpha\end{bmatrix} and B=[β110], α,β∈RB=\begin{bmatrix}\beta&1\\1&0\end{bmatrix},\ \alpha,\beta\in\mathbf{R}. Let…MediumNumerical value
  3. 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

2021 3 questions

  1. 25 Jul 2021, Shift 1 · Q87Let…MediumNumerical value
  2. 16 Mar 2021, Shift 2 · Q88Let A=[a1a2]A=\begin{bmatrix}a_1\\a_2\end{bmatrix} and B=[b1b2]B=\begin{bmatrix}b_1\\b_2\end{bmatrix} be two 2×12\times1 matrices with real entries…MediumNumerical value
  3. 18 Mar 2021, Shift 1 · Q63Let A+2B=[1206−33−531]A+2B=\begin{bmatrix}1&2&0\\6&-3&3\\-5&3&1\end{bmatrix} and 2A−B=[2−152−16012]2A-B=\begin{bmatrix}2&-1&5\\2&-1&6\\0&1&2\end{bmatrix}. If Tr(A)…EasySingle correct

2020 2 questions

  1. 8 Jan 2020, Shift 1 · Q72The number of all 3×33\times3 matrices A, with enteries from the set {−1,0,1}\{-1,0,1\} such that the sum of the diagonal elements of AATAA^T is…MediumNumerical value
  2. 2 Sep 2020, Shift 1 · Q54Let AA be a 2×22\times2 real matrix with entries from {0,1}\{0, 1\} and ∣A∣≠0|A|\neq0. Consider the following two statements : (P) If…MediumTwo statements

Pattern: Asked most years.