JEE Main 2020MathematicsMatricesMediumMCQ

JEE Main 2020 — Matrices Question with Solution

JEE Main 2020 (07 Jan Shift 1)

Question

Let α be a root of the equation x2+x+1=0 and the matrix A=131111αα21α2α4, then the matrix A31 is equal to

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Show full solutionCorrect option: A
Correct answer
AA3

Step-by-step explanation

Here, α=ω,ω2 where ω is complex cube root of unity.

A2=131111ωω21ω2ω1111ωω21ω2ω=100001010

⇒A4=100001010100001010=100010001

⇒A31=A28×A3=I×A3=A3

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About this question

This is a previous-year question from JEE Main 2020, 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.