JEE Main 2024MathematicsMatricesEasyNumerical

JEE Main 2024 — Matrices Question with Solution

JEE Main 2024 (31 Jan Shift 2)

Question

Let A be a 3×3 matrix and detA=2. If  n=detadjadj....adjA⏟2024−times, then the remainder when n is divided by 9 is equal to __________.

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Show full solutionCorrect answer: 7
Correct answer
7

Step-by-step explanation

Given,

A=2

And n=detadjadjadj...A⏟2024 times

Now, using the formula adjadjadj...A⏟r times=An−1r we get,

adjadjadj...A⏟2024 times=An−12024

⇒n=A22024

⇒n=222024 as A=2

Now, solving

22024=41012=3+11012=3k+1

⇒222024=23k+1

⇒222024=2·23k

⇒222024=2·9-1k

⇒222024=9m-2

⇒222024=9t-2+9

⇒222024=9m+7

Hence, the remainder is 7

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About this question

This is a previous-year question from JEE Main 2024, 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.