JEE Main 2023MathematicsMatricesMediumMCQ

JEE Main 2023 — Matrices Question with Solution

JEE Main 2023 (13 Apr Shift 2)

Question

Let for A=123α31112,A=2. If |2adj(2adj(2A))|=32n, then 3n+α is equal to

Choose an option

Show full solutionCorrect option: B
Correct answer
B11

Step-by-step explanation

Given that A=123α31112

⇒|A|=2

⇒16-1-α-7=2

⇒-α-2=2

⇒α=-4

⇒|2adj(2adj(2A))|=32n

We know that kA=knA, adj(adj(A))=An-12 and adjkA=kn-1adjA.

=23|adj(2adj(2A))|

=23|23-1adj(adj(2A))|

=23·(4)3|adj(adj(2A))|

=29|2A|(2)2

=29·|2A|4

=29·212|A|4

=221·24=225=(32)n=(2)5n

∴n=5

⇒3n+α=15-4=11

Hence this is the correct option.

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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.