JEE Main 2022 · MathsNumerical answerNumerical valueMediumCalculation

JEE Main 28 July 2022, Shift 1, Maths Q25

Question 25 of 90 in this shift, Maths question 25 of 30, Section B.

Let

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

\alpha_1

be the value of

\alpha

which satisfies

(A+B)^2=A^2+\begin{bmatrix}2&2\\2&2\end{bmatrix}

and

\alpha_2

be the value of

\alpha

which satisfies

(A+B)^2=B^2

. Then

|\alpha_1-\alpha_2|

is equal to __________.

Official answer

NTA final key (2022 Session 2).

Chapter: Matrices
Topic: Matrix Multiplication
Idea tested: Binomial Expansion for Non-Commuting Matrices

Same topic in other shifts

All Matrix Multiplication questions

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

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.