JEE Main 2023MathematicsMatricesMediumMCQ

JEE Main 2023 — Matrices Question with Solution

JEE Main 2023 (24 Jan Shift 1)

Question

If A and B are two non-zero n×n matrices such that A2+B=A2B, then

Choose an option

Show full solutionCorrect option: D
Correct answer
DA2B=BA2

Step-by-step explanation

Given:

A2B=A2+B

⇒A2B-A2-B+I=I

⇒A2B-I-B-I=I

⇒A2-IB-I=I

⇒A2-IB-IB-I-1=IB-I-1

⇒A2-I=B-I-1

Also,

A2+B=A2B

⇒A2B-I=B

⇒A2=BB-I-1

⇒A2=BA2-I

⇒A2=BA2-B

⇒A2+B=BA2

⇒A2B=BA2

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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.