JEE Main 2022 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 25 June 2022, Shift 1, Maths Q11

Question 11 of 90 in this shift, Maths question 11 of 30, Section A.

Let

A=\begin{bmatrix}0&-2\\2&0\end{bmatrix}

. If M and N are two matrices given by

M=\sum_{k=1}^{10}A^{2k}

and

N=\sum_{k=1}^{10}A^{2k-1}

then

MN^2

is :

(1)a non-identity symmetric matrixOfficial answer
(2)a skew-symmetric matrix
(3)neither symmetric nor skew-symmetric matrix
(4)an identity matrix

Official answer

Option 1

NTA final key.

Chapter: Matrices
Topic: Matrix Multiplication
Idea tested: Powers of Skew-Symmetric Matrices

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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.