JEE Main 2014MathematicsMatricesMediumMCQ

JEE Main 2014 — Matrices Question with Solution

JEE Main 2014 (09 Apr Online)

Question

If B is a 3×3  matrix such that B2=0, then det. I+B50-50B is equal to :

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Show full solutionCorrect option: A
Correct answer
A1

Step-by-step explanation

B2=0⇒B4=B6=B8=....=B50=0  and B3=B2B=0B=0

⇒ I+B50=I+C150B (higher powers are zero)

∴ det.I+B50-50B 

  =det. I+50C1B-50B

  =det.I

  =1

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About this question

This is a previous-year question from JEE Main 2014, 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.