JEE Main 2021MathematicsMatricesEasyNumerical

JEE Main 2021 — Matrices Question with Solution

JEE Main 2021 (18 Mar Shift 2)

Question

Let I be an identity matrix of order 2×2 and P=2-15-3. Then the value of n∈N for which Pn=5I-8P is equal to ___ .

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Show full solutionCorrect answer: 6
Correct answer
6

Step-by-step explanation

P=2-15-3

5I-8P=5005-16-840-24=-118-4029

P2=2-15-32-15-3=-11-54

P3=2-15-3-11-54=3-210-7

⇒P6=3-210-73-210-7=-118-4029=Pn

⇒n=6

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About this question

This is a previous-year question from JEE Main 2021, 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.