JEE Main 2014MathematicsMatricesEasyMCQ

JEE Main 2014 — Matrices Question with Solution

JEE Main 2014 (06 Apr)

Question

If A is a 3×3 non-singular matrix such that AA'=A'A and B=A-1A', then BB' equals, where X' denotes the transpose of the matrix X.

Choose an option

Show full solutionCorrect option: D
Correct answer
DI

Step-by-step explanation

A'=AT

AA'=A'A

B=A-1A'

B'=A-1A''=A''·A-1'=AA-1'

BB'=A-1A'·AA-1'

       =A-1·A·A'·A-1'     ∵  AA'=A'A

       =I·A'·A-1'

       =I·A-1A'           ∵  CD'=D'C'

       =I·I'

       =I2                                      ∵  I=I'

       =I

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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.