JEE Main 2024 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 9 April 2024, Shift 2, Maths Q4

Question 4 of 90 in this shift, Maths question 4 of 30, Section A.

Let

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

C^4+\alpha C^2+\beta I=O

, then

2\beta-\alpha

is equal to

(1) $2$
(2) $8$
(3) $10$ Official answer
(4) $16$

Official answer

Option 3

NTA final key.

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

Same idea in other shifts

Asked 4× 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

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 42 of the 174 JEE Main shifts held from 2017 to 2026.