JEE Main Maths · Matrices

Matrix Multiplication in JEE Main

Name: Matrix Multiplication: JEE Main previous year questions
Creator: Lumi

Matrix Multiplication (Maths, Matrices) came 19 times in 17 of the 42 JEE Main shifts Lumi analysed, across 11 distinct ideas. 10 of them came in 2024–26; it was last asked in 2026.

Questions: 19; in 17 shifts
Ideas asked: 11; 2 asked more than once
Numerical answer: 7; 37% of its questions
Pattern: Asked most years; last asked 2026

Questions each year

In the shifts Lumi analysed for each year.

Difficulty and format

Easy 0Medium 13Hard 6

Format

Single correct11 Q
Numerical value7 Q
Other1 Q

Ideas inside the topic

11 ideas

Powers of Square Matrices6 Q
Cayley-Hamilton Theorem Application4 Q
Binomial Expansion for Commuting Matrices1 Q
Binomial Expansion for Non-Commuting Matrices1 Q
Idempotent and Nilpotent Matrices1 Q
Involutory Matrix Properties1 Q
Row-by-Column Multiplication1 Q
Orthogonal Matrix Multiplication Definition1 Q
Matrix Polynomials1 Q
Trace of A times A Transpose1 Q
Transpose Reversal Law1 Q

Where it sits

Part of Matrices, which had 28 questions in all. Matrix Multiplication accounts for 68% of them. In Lumi's JEE taxonomy it belongs to Algebra.

Every question

All 19 Matrix Multiplication questions

Newest first, each with its options and official answer.

2 Apr 2026, Shift 1 · Q4Let $A=\begin{bmatrix}1&2\\1&\alpha\end{bmatrix}$ and $B=\begin{bmatrix}3&3\\\beta&2\end{bmatrix}$ . If $A^2-4A+I=O$ and $B^2-5B-6I=O$ ,…HardOther
4 Apr 2026, Shift 1 · Q5Let $S=\left\{A=\begin{bmatrix}a&b\\c&d\end{bmatrix}: a,b,c,d\in\{0,1,2,3,4\}\text{ and }A^2-4A+3I=0\right\}$ be a set of $2\times2$ …HardSingle correct
6 Apr 2026, Shift 2 · Q5Let $A=\begin{bmatrix}1&0&0\\3&1&0\\9&3&1\end{bmatrix}$ and $B=[b_{ij}]$ , $1\le i,j\le 3$ . If $B=A^{99}-I$ , then the value of…MediumSingle correct
2 Apr 2025, Shift 1 · Q18Let $A=\begin{bmatrix}\alpha&-1\\6&\beta\end{bmatrix}$ , $\alpha>0$ , such that $\det(A)=0$ and $\alpha+\beta=1$ . If I denotes $2\times2$ …MediumSingle correct
2 Apr 2025, Shift 2 · Q3Let $A$ be a $3\times3$ real matrix such that $A^2(A-2I) - 4(A-I) = O$ , where $I$ and $O$ are the identity and null matrices,…MediumSingle correct
4 Apr 2025, Shift 2 · Q4Let the matrix $A=\begin{bmatrix}1&0&0\\1&0&1\\0&1&0\end{bmatrix}$ satisfy $A^n=A^{n-2}+A^2-I$ for $n\ge 3$ . Then the sum of all the…HardSingle correct
8 Apr 2024, Shift 1 · Q4Let $A=\begin{bmatrix}2&a&0\\1&3&1\\0&5&b\end{bmatrix}$ . If $A^3=4A^2-A-21I$ , where $I$ is the identity matrix of order $3\times3$ , then…MediumSingle correct
8 Apr 2024, Shift 1 · Q22Let $A=\begin{bmatrix}2&-1\\1&1\end{bmatrix}$ . If the sum of the diagonal elements of $A^{13}$ is $3^n$ , then $n$ is equal to ____________.MediumNumerical value
9 Apr 2024, Shift 2 · Q4Let $B=\begin{bmatrix}1&3\\1&5\end{bmatrix}$ and $A$ be a $2\times2$ matrix such that $AB^{-1}=A^{-1}$ . If $BCB^{-1}=A$ and…HardSingle correct
29 Jan 2024, Shift 1 · Q4Let A be a square matrix such that $AA^T=I$ . Then $\frac{1}{2}A\left[(A+A^T)^2+(A-A^T)^2\right]$ is equal toMediumSingle correct
6 Apr 2023, Shift 1 · Q3Let $A=[a_{ij}]_{2\times2}$ , where $a_{ij}\neq0$ for all i, j and $A^2=I$ . Let $a$ be the sum of all diagonal elements of $A$ and $b=|A|$ .…MediumSingle correct
11 Apr 2023, Shift 1 · Q6Let $A$ be a $2 \times 2$ matrix with real entries such that $A' = \alpha A + I$ , where $\alpha \in \mathbb{R} - \{-1, 1\}$ . If…MediumSingle correct
11 Apr 2023, Shift 1 · Q29Let $A = \begin{bmatrix} 0 & 1 & 2 \\ a & 0 & 3 \\ 1 & c & 0 \end{bmatrix}$ , where $a, c \in \mathbb{R}$ . If $A^3 = A$ and the positive…HardNumerical value
25 Jul 2022, Shift 1 · Q21Let $A=\begin{pmatrix}2&-1&-1\\1&0&-1\\1&-1&0\end{pmatrix}$ and $B=A-I$ . If $\omega=\frac{\sqrt3\,i-1}{2}$ , then the number of elements in…HardNumerical value
28 Jul 2022, Shift 1 · Q25Let $A=\begin{bmatrix}1&-1\\2&\alpha\end{bmatrix}$ and $B=\begin{bmatrix}\beta&1\\1&0\end{bmatrix},\ \alpha,\beta\in\mathbf{R}$ . Let…MediumNumerical value
29 Jun 2022, Shift 1 · Q10Let $A = [a_{ij}]$ be a square matrix of order 3 such that $a_{ij} = 2^{j-i}$ , for all $i, j = 1, 2, 3$ . Then, the matrix…MediumSingle correct
25 Jul 2021, Shift 1 · Q87Let…MediumNumerical value
16 Mar 2021, Shift 2 · Q88Let $A=\begin{bmatrix}a_1\\a_2\end{bmatrix}$ and $B=\begin{bmatrix}b_1\\b_2\end{bmatrix}$ be two $2\times1$ matrices with real entries…MediumNumerical value
8 Jan 2020, Shift 1 · Q72The number of all $3\times3$ matrices A, with enteries from the set $\{-1,0,1\}$ such that the sum of the diagonal elements of $AA^T$ is…MediumNumerical value