JEE Main 2022MathematicsMatricesHardNumerical

JEE Main 2022 — Matrices Question with Solution

JEE Main 2022 (25 Jul Shift 1)

Question

Let A=2-1-110-11-10 and B=A-I. If ω=3i-12, then the number of elements in the set n∈1,2,…,100:An+ωBn=A+B is equal to _____ .

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Show full solutionCorrect answer: 17
Correct answer
17

Step-by-step explanation

Given, A=2-1-110-11-10

⇒A2=2-1-110-11-102-1-110-11-10=2-1-110-11-10=A

⇒An=A 

Now ∀n∈1,2,…,100

Now, B=A-I=1-1-11-1-11-1-1

B2=1-1-11-1-11-1-11-1-11-1-11-1-1=-1-1-11-1-11-1-1=-B 

⇒B3=-B2=B 

⇒B5=B 

⇒B99=B

Also, ω3k=1

So, n= common of 1,3,5,…,99 and  3,6,9,…,99=17

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About this question

This is a previous-year question from JEE Main 2022, covering the Matrices chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.