JEE Main 2024MathematicsMatricesEasyMCQ

JEE Main 2024 — Matrices Question with Solution

JEE Main 2024 (29 Jan Shift 2)

Question

Let A=2126211332 and P=120502715. The sum of the prime factors of P-1AP-2I is equal to

Choose an option

Show full solutionCorrect option: A
Correct answer
A26

Step-by-step explanation

Let, y=P-1AP-2I

⇒y=P-1AP-2P-1P

⇒y=P-1I( A-2I)P

⇒y=P-1I|A-2I||P|

We know that, A=1A-1.

⇒y=|A-2I|

⇒y=2126211332-200020002

⇒y=0126011330

⇒y=0-0-33+218-0

⇒y=69

Now, prime factor of 69 is 3 and 23.

So, sum =26

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About this question

This is a previous-year question from JEE Main 2024, 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.