JEE Main Maths · Determinants

Matrix Inverse in JEE Main

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

Matrix Inverse (Maths, Determinants) came 22 times in 21 of the 42 JEE Main shifts Lumi analysed, across 7 distinct ideas. 17 of them came in 2024–26; it was last asked in 2026.

Questions: 22; in 21 shifts
Ideas asked: 7; 5 asked more than once
Numerical answer: 6; 27% 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 15Hard 7

Format

Single correct15 Q
Numerical value6 Q
Other1 Q

Ideas inside the topic

7 ideas

Inverse Relation to Double Adjoint8 Q
Trap involving |adj(A)| vs |A^-1|6 Q
Cofactor Matrix and Adjoint2 Q
Solving Matrix Equations2 Q
Singular and Non-singular Matrices2 Q
Commutativity of Adjoint and Inverse1 Q
Inverse via Characteristic Equation1 Q

Where it sits

Part of Determinants, which had 59 questions in all. Matrix Inverse accounts for 37% of them. In Lumi's JEE taxonomy it belongs to Algebra.

Some questions sit in other chapters too: Matrices.

Every question

All 22 Matrix Inverse questions

Newest first, each with its options and official answer.

2 Apr 2026, Shift 2 · Q22Consider the matrices $A = \begin{bmatrix} 2 & -2 \\ 4 & -2 \end{bmatrix}$ and $B = \begin{bmatrix} -3 & 9 \\ 1 & 3 \end{bmatrix}$ . If…MediumNumerical value
4 Apr 2026, Shift 1 · Q6Let $A=\begin{bmatrix}1&1&2\\-2&0&1\\1&3&5\end{bmatrix}$ . Then the sum of all elements of the matrix…MediumSingle correct
5 Apr 2026, Shift 1 · Q3Let A be a $3 \times 3$ matrix such that $A^T\begin{bmatrix}1\\0\\1\end{bmatrix}=\begin{bmatrix}5\\2\\2\end{bmatrix}$ ,…HardSingle correct
5 Apr 2026, Shift 2 · Q4Let M be a $3\times 3$ matrix such that $M\begin{pmatrix}1\\0\\0\end{pmatrix}=\begin{pmatrix}1\\2\\3\end{pmatrix}$ ,…MediumSingle correct
6 Apr 2026, Shift 1 · Q21Let $A=\begin{bmatrix}-1&1&-1\\1&0&1\\0&0&1\end{bmatrix}$ satisfy…MediumNumerical value
6 Apr 2026, Shift 2 · Q17Let $A=\begin{bmatrix}1&3&-1\\2&1&\alpha\\0&1&-1\end{bmatrix}$ be a singular matrix. Let $f(x)=\int_0^x\left(t^2+2t+3\right)dt$ ,…MediumSingle correct
8 Apr 2026, Shift 2 · Q4Let $A = \begin{bmatrix} \alpha & 1 & 2 \\ 2 & 3 & 0 \\ 0 & 4 & 5 \end{bmatrix}$ and…HardSingle correct
2 Apr 2025, Shift 1 · Q15Let $a\in\mathbf{R}$ and A be a matrix of order $3\times3$ such that $\det(A)=-4$ and…MediumSingle correct
3 Apr 2025, Shift 1 · Q5Let $A$ be a matrix of order $3 \times 3$ and $|A| = 5$ . If $|2\,adj(3A\,adj(2A))| = 2^{\alpha}\cdot 3^{\beta}\cdot 5^{\gamma}$ ,…MediumSingle correct
3 Apr 2025, Shift 2 · Q22Let I be the identity matrix of order $3 \times 3$ and for the matrix…HardNumerical value
7 Apr 2025, Shift 1 · Q5Let $A$ be a $3 \times 3$ matrix such that $|\mathrm{adj}(\mathrm{adj}(\mathrm{adj}\,A))| = 81$ . If…HardSingle correct
7 Apr 2025, Shift 1 · Q22The number of singular matrices of order 2, whose elements are from the set $\{2, 3, 6, 9\}$ , is ___________.MediumNumerical value
8 Apr 2025, Shift 2 · Q4Let $A = \begin{bmatrix} 2 & 2+p & 2+p+q \\ 4 & 6+2p & 8+3p+2q \\ 6 & 12+3p & 20+6p+3q \end{bmatrix}$ . If…MediumSingle correct
6 Apr 2024, Shift 2 · Q4If $A$ is a square matrix of order 3 such that $\det(A)=3$ and…MediumSingle correct
9 Apr 2024, Shift 1 · Q23Let A be a non-singular matrix of order 3. If $\det(3\,\mathrm{adj}(2\,\mathrm{adj}((\det A)A)))=3^{-13}\cdot2^{-10}$ and…HardNumerical value
30 Jan 2024, Shift 2 · Q3Let $R = \begin{pmatrix} x & 0 & 0 \\ 0 & y & 0 \\ 0 & 0 & z \end{pmatrix}$ be a non-zero $3\times 3$ matrix, where…HardOther
31 Jan 2024, Shift 2 · Q22Let A be a $3\times3$ matrix and $\det(A)=2$ . If…MediumNumerical value
8 Apr 2023, Shift 2 · Q4If $A = \begin{bmatrix} 1 & 5 \\ \lambda & 10 \end{bmatrix}$ , $A^{-1} = \alpha A + \beta I$ and $\alpha + \beta = -2$ , then…MediumSingle correct
13 Apr 2023, Shift 2 · Q5Let for $A=\begin{bmatrix}1&2&3\\ \alpha&3&1\\ 1&1&2\end{bmatrix}$ , $|A|=2$ . If $|2\,\mathrm{adj}(2\,\mathrm{adj}(2A))|=32^n$ , then…MediumSingle correct
28 Jul 2022, Shift 1 · Q14Let the matrix $A=\begin{bmatrix}0&1&0\\0&0&1\\1&0&0\end{bmatrix}$ and the matrix $B_0=A^{49}+2A^{98}$ . If $B_n=\mathrm{Adj}(B_{n-1})$ for…HardSingle correct
24 Jun 2022, Shift 1 · Q9Let $S = \{\sqrt{n} : 1 \le n \le 50$ and n is odd $\}$ . Let $a \in S$ and…MediumSingle correct
2 Apr 2017 (offline) · Q64If $A=\begin{bmatrix}2&-3\\-4&1\end{bmatrix}$ , then $\mathrm{adj}(3A^2+12A)$ is equal to :MediumSingle correct