JEE Main 2021MathematicsMatricesMediumMCQ

JEE Main 2021 — Matrices Question with Solution

JEE Main 2021 (26 Aug Shift 1)

Question

If A=1525-2515,B=10i1,i=-1, and Q=ATBA, then the inverse of the matrix AQ2021AT is equal to:

Choose an option

Show full solutionCorrect option: B
Correct answer
B10-2021i1

Step-by-step explanation

AA⊤=1525-251515-252515=1001=I

Q=A⊤BA

⇒Q2=A⊤BAA⊤BA

=A⊤BAA⊤BA

=A⊤BIBA

=A⊤B2A

⇒Q3=A⊤B3A

⇒Q2021=ATB2021 A

Now let P=AQ2021 AT

P=AA⊤B2021 AA⊤

given AA⊤=I

P=B2021

B2=10i110i1=102i1

B3=102110i1=103i1

B2021=102021i1

inverse of P=P-1=B2021-1=10-2021i1

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 2021, 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.