JEE Main 2022MathematicsMatricesEasyMCQ

JEE Main 2022 — Matrices Question with Solution

JEE Main 2022 (27 Jul Shift 2)

Question

Let A=4-2αβ. If A2+γA+18I=O, then detA is equal to _______.

Choose an option

Show full solutionCorrect option: B
Correct answer
B18

Step-by-step explanation

Given A=4-2αβ ⇒detA=4β+2α

Characteristic equation of the matrix is 

4-λ-2αβ-λ=0

⇒4β+λ2-β+4λ+2α=0

⇒λ2-β+4λ+2α+4β=0

Comparing with given equation A2+γA+18I=0, we get

⇒γ=-β+4 & 2α+4β=18

Hence detA=4β+2α=18

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About this question

This is a previous-year question from JEE Main 2022, 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.