JEE Main 2018MathematicsMatricesMediumMCQ

JEE Main 2018 — Matrices Question with Solution

JEE Main 2018 (15 Apr)

Question

Let A be a matrix such that A·1203 is a scalar matrix and 3A=108. Then, A2 equals :

Choose an option

Show full solutionCorrect option: B
Correct answer
B36-3204

Step-by-step explanation

Let A=abcd

Now, A.1203=abcd1203=a2a+3bc2c+3d is a scalar.

∴ c =0, 2a+3b=0, a=2c+3d⇒a=3d

Given, 3A=108

⇒A=10832=12⇒ad-bc=ad=12

⇒3dd=12⇒d2=4 ∵a=3d

∴ a2=3d2=9d2==9×4=36 and

∵ 2a+3b=0⇒b=-2a3=-2×63⇒b=-4

Now, A2=ab0dab0d=a2ab+bd0d2=36-3204

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About this question

This is a previous-year question from JEE Main 2018, 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.