JEE Main 2021 · MathsNumerical answerNumerical valueMediumMulti-step

JEE Main 31 August 2021, Shift 2, Maths Q81

Question 81 of 90 in this shift, Maths question 21 of 30, Section B.

The number of elements in the set

\left\{\mathrm{A} = \begin{pmatrix}\mathrm{a} & \mathrm{b}\\ 0 & \mathrm{d}\end{pmatrix} : \mathrm{a}, \mathrm{b}, \mathrm{d} \in \{-1, 0, 1\} \text{ and } (\mathrm{I}-\mathrm{A})^3 = \mathrm{I}-\mathrm{A}^3\right\}

, where I is

2\times 2

identity matrix, is ______________.

Official answer

NTA final key.

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

Same idea in other shifts

Asked 3× in all

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
29 Jun 2022, Shift 2 · Q3Let $A = \begin{pmatrix} 2 & -1 \\ 0 & 2 \end{pmatrix}$ . If $B = I - {}^5C_1\,(adjA) + {}^5C_2\,(adjA)^2 - \ldots - {}^5C_5\,(adjA)^5$ ,…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 108 of the 174 JEE Main shifts held from 2017 to 2026.