Matrices JEE Main PYQs PDF, 2020–2026

Matrices questions per year

Topic-wise weightage by year

How many Matrices questions each topic had in every JEE Main year (all shifts), counting every question asked, including ones not in the PDF. Darker cells mean more questions.

Swipe the table sideways for older years.

Newest questions (2026)

The 12 newest of the 13 JEE Main 2026 Matrices questions in the free PDF, latest shift first.

1. JEE Main 2026 · 6 Apr · Shift 2 · Types of Matrices and Operations

   Let ${\mathrm{A}}=\left[\begin{array}{ccc}1 & 0 & 0 \\ 3 & 1 & 0 \\ 9 & 3 & 1\end{array}\right]$ and ${\mathrm{B}}=[{\mathrm{b}}_{{ij}}],1\leq i,j\leq 3$. If ${\mathrm{B}}={\mathrm{A}}^{{99}}-{\mathrm{I}}$, then the value of $\frac{{\mathrm{b}}_{{31}}-{\mathrm{b}}_{{21}}}{{\ \mathrm{b}}_{{32}}}$ is :

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2. JEE Main 2026 · 5 Apr · Shift 1 · Types of Matrices and Operations

   Let A be a $3\times 3$ matrix such that

   ${\mathrm{A}}^{{{\mathrm{T}}}}\left[\begin{array}{c}1 \\ 0 \\ 1\end{array}\right]=\left[\begin{array}{c}5 \\ 2 \\ 2\end{array}\right],{\mathrm{A}}^{{{\mathrm{T}}}}\left[\begin{array}{c}0 \\ 0 \\ 1\end{array}\right]=\left[\begin{array}{c}3 \\ 1 \\ 1\end{array}\right],{\mathrm{A}}\left[\begin{array}{c}1 \\ 0 \\ 1\end{array}\right]=\left[\begin{array}{c}3 \\ 4 \\ 4\end{array}\right]\text{ and}{\mathrm{A}}\left[\begin{array}{c}0 \\ 0 \\ 1\end{array}\right]=\left[\begin{array}{c}1 \\ 3 \\ 1\end{array}\right].$

   If $\det (A)=1$, then $\det \left(\mathrm{adj}\left(A^{2}+A\right)\right)$ is equal to:

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3. JEE Main 2026 · 5 Apr · Shift 2 · Types of Matrices and Operations

   Let M be a $3\times 3$ matrix such that ${\mathrm{M}}\left(\begin{array}{c}1 \\ 0 \\ 0\end{array}\right)=\left(\begin{array}{c}1 \\ 2 \\ 3\end{array}\right),{\mathrm{M}}\left(\begin{array}{c}0 \\ 1 \\ 0\end{array}\right)=\left(\begin{array}{c}0 \\ 1 \\ 2\end{array}\right)$ and ${\mathrm{M}}\left(\begin{array}{c}0 \\ 0 \\ 1\end{array}\right)=\left(\begin{array}{c}-1 \\ 1 \\ 1\end{array}\right)$. If ${\mathrm{M}}\left(\begin{array}{c}x \\ y \\ z\end{array}\right)=\left(\begin{array}{c}1 \\ 7 \\ 11\end{array}\right)$, then $x+y+z$ equals :

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4. JEE Main 2026 · 4 Apr · Shift 1 · Types of Matrices and Operations

   Let ${\mathrm{S}}=\left\{{\mathrm{A}}=\left[\begin{array}{cc}a & b \\ c & d\end{array}\right]:a,b,c,d\in \{0,1,2,3,4\}\right.$ and $\left.{\mathrm{A}}^{2}-4{\ \mathrm{A}}+3{\mathrm{I}}=0\right\}$ be a set of $2\times 2$ 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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5. JEE Main 2026 · 2 Apr · Shift 1 · Types of Matrices and Operations

   Let $A=\left[\begin{array}{cc}1 & 2 \\ 1 & \alpha\end{array}\right]$ and $B=\left[\begin{array}{cc}3 & 3 \\ \beta & 2\end{array}\right]$. If $A^{2}-4A+I=O$ and $B^{2}-5B-6I=O$, then among the two statements:

   (S1) : $[(B-A)(B+A)]^{T}=\left[\begin{array}{cc}13 & 15 \\ 7 & 10\end{array}\right]$

   and

   (S2) : $det({\mathrm{adj}}(A+B))=-5$

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6. JEE Main 2026 · 2 Apr · Shift 2 · Inverse of a Matrix

   Consider the matrices $A=\left[\begin{array}{cc}2 & -2 \\ 4 & -2\end{array}\right]$ and $B=\left[\begin{array}{cc}3 & 9 \\ 1 & 3\end{array}\right]$. If matrices $P$ and $Q$ are such that $PA=B$ and $AQ=B$, then the absolute value of the sum of the diagonal elements of $2(P+Q)$ is ________.

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7. JEE Main 2026 · 28 Jan · Shift 2 · Types of Matrices and Operations

   Let $A=\left[\begin{array}{cc}3 & -4 \\ 1 & -1\end{array}\right]$ and $B$ be two matrices such that $A^{{100}}=100B+I$. Then the sum of all the elements of $B^{{100}}$ is _______

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8. JEE Main 2026 · 28 Jan · Shift 1 · Inverse of a Matrix

   Let $A,B$ and $C$ be three $2\times 2$ matrices with real entries such that $B=(I+A)^{{-1}}$ and ${\mathrm{A}}+{\mathrm{C}}={\mathrm{I}}$.
   
   If ${\mathrm{BC}}=\left[\begin{array}{cc}1 & -5 \\ -1 & 2\end{array}\right]$ and ${\mathrm{CB}}\left[\begin{array}{c}x_{1} \\ x_{2}\end{array}\right]=\left[\begin{array}{c}12 \\ -6\end{array}\right]$, then $x_{1}+x_{2}$ is

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9. JEE Main 2026 · 24 Jan · Shift 1 · Types of Matrices and Operations

   The number of $3\times 2$ matrices A , which can be formed using the elements of the set $\{-2,-1,0,1,2\}$ such that the sum of all the diagonal elements of ${\mathrm{A}}^{{{\mathrm{T}}}}{\mathrm{A}}$ is 5 , is

   $\_\_\_\_$

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10. JEE Main 2026 · 23 Jan · Shift 2 · Inverse of a Matrix

    Let $A=\left[\begin{array}{ccc}0 & 2 & -3 \\ -2 & 0 & 1 \\ 3 & -1 & 0\end{array}\right]$ and $B$ be a matrix such that $B(I-A)=I+A$. Then the sum of the diagonal elements of ${\mathrm{B}}^{{{\mathrm{T}}}}{\mathrm{B}}$ is equal to $\_\_\_\_$

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11. JEE Main 2026 · 22 Jan · Shift 1 · Types of Matrices and Operations

    If ${\mathrm{A}}=\left[\begin{array}{cc}2 & 3 \\ 3 & 5\end{array}\right]$, then the determinant of the matrix $\left({\mathrm{A}}^{{2025}}-3{\ \mathrm{A}}^{{2024}}+{\mathrm{A}}^{{2023}}\right)$ is

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12. JEE Main 2026 · 21 Jan · Shift 1 · Types of Matrices and Operations

    For some $\alpha,\beta\in {\mathbf{R}}$, let $A=\left[\begin{array}{cc}\alpha & 2 \\ 1 & 2\end{array}\right]$ and $B=\left[\begin{array}{cc}1 & 1 \\ 1 & \beta\end{array}\right]$ be such that $A^{2}-4A+2I=B^{2}-3B+I=O$. Then $\left(\det \left(\mathrm{adj}\left(A^{3}-B^{3}\right)\right)\right)^{2}$ is equal to $\_\_\_\_$ .

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