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JEE Main 2022 · MathsNumerical answerNumerical valueMediumMulti-step

JEE Main 25 June 2022, Shift 2, Maths Q21

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

Let

A = \begin{pmatrix} 2 & -2 \\ 1 & -1 \end{pmatrix}

and

B = \begin{pmatrix} -1 & 2 \\ -1 & 2 \end{pmatrix}

. Then the number of elements in the set

\{(n, m) : n, m \in \{1, 2, ........, 10\}

and

nA^n + mB^m = I\ \}

is ____________.

Official answer

1

NTA final key.

Chapter: Matrices
Topic: Matrix Multiplication
Idea tested: Idempotent and Nilpotent Matrices

Same idea in other shifts

Asked 2× in all

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

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.