JEE Main 2024 · MathsNumerical answerNumerical valueMediumMulti-step

JEE Main 4 April 2024, Shift 2, Maths Q23

Question 23 of 90 in this shift, Maths question 23 of 30, Section B.

Let

A

be a

2\times2

symmetric matrix such that

A\begin{bmatrix}1\\1\end{bmatrix}=\begin{bmatrix}3\\7\end{bmatrix}

and the determinant of

A

be 1. If

A^{-1}=\alpha A+\beta I

, where

I

is an identity matrix of order

2\times2

, then

\alpha+\beta

equals __________

Official answer

NTA final key.

Chapter: Determinants
Topic: Matrix Multiplication
Idea tested: Cayley-Hamilton Theorem Application

Same idea in other shifts

Asked 10× in all

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
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
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
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
27 Jul 2022, Shift 1 · Q4Let $A = \begin{pmatrix} 1 & 2 \\ -2 & -5 \end{pmatrix}$ . Let $\alpha, \beta \in \mathbb{R}$ be such that $\alpha A^2 + \beta A = 2I$ .…MediumSingle correct
27 Jul 2022, Shift 2 · Q4Let $A = \begin{pmatrix} 4 & -2 \\ \alpha & \beta \end{pmatrix}$ . If $A^2 + \gamma A + 18I = O$ , then det (A) is equal to __________.MediumSingle correct
27 Aug 2021, Shift 1 · Q63If the matrix $A=\begin{pmatrix}0 & 2\\ K & -1\end{pmatrix}$ satisfies $A(A^3+3I)=2I$ , then the value of $K$ is :MediumSingle correct
26 Feb 2021, Shift 2 · Q86If the matrix $A=\begin{bmatrix} 1 & 0 & 0 \\ 0 & 2 & 0 \\ 3 & 0 & -1 \end{bmatrix}$ satisfies the equation…HardNumerical value

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.