JEE Main 2023MathematicsMatricesMediumNumerical

JEE Main 2023 — Matrices Question with Solution

JEE Main 2023 (31 Jan Shift 2)

Question

Let A be a n×n matrix such that A=2. If the determinant of the matrix Adj2.Adj2 A-1 is 284, then n is equal to _____ .

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Show full solutionCorrect answer: 5
Correct answer
5

Step-by-step explanation

Given,

A=2

Now simplifying,

Adj2.Adj2 A-1

=2·Adj2 A-1n-1

=2nAdj2 A-1n-1

=2n2A-1n-1n-1

=2nn-12nA-1n-1n-1

∴   A-1=1A=12

=2nn-12n-1n-1n-1

=2nn-1+n-13=284

Now comparing both side we get,

nn-1+n-13=84

⇒n-1n+n2-2n+1=84

⇒n-1n2-n+1=4×21

Now if n-1=4⇒n=5 now checking n2-3n+1=25-5+1=21

Hence, n=5

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About this question

This is a previous-year question from JEE Main 2023, 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.