JEE Main 2019MathematicsMatricesMediumMCQ

JEE Main 2019 — Matrices Question with Solution

JEE Main 2019 (09 Apr Shift 2)

Question

The total number of matrices A=02y12xy-12x-y1, x, y∈R, x≠y for which ATA=3I3 is:

Choose an option

Show full solutionCorrect option: C
Correct answer
C4

Step-by-step explanation

Given ATA=3I3

02x2x2yy-y1-1102y12xy-12x-y1=300030003

8x20006y20003=300030003

On comparing the two matrices, we get

8x2=3 and 6y2=3

⇒x2=38 and y2=12

⇒x=±38 and y=±12

For each of x & y we have two possible values, hence there are total 2×2=4 combinations of values are possible.

Hence, total 4 matrices are possible.

Practice this on the real CBT interface

Solve this JEE Main question (and the rest of the Matrices chapter) on PrepSharp's TCS iON-style CBT player — with timer, bookmarks and session analytics.

Solve interactively →

About this question

This is a previous-year question from JEE Main 2019, 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.