JEE Main 2014MathematicsMatricesEasyMCQ

JEE Main 2014 — Matrices Question with Solution

JEE Main 2014 (19 Apr Online)

Question

Let A and B be any two 3 × 3  matrices. If A is symmetric and B is skew symmetric, then the matrix AB-BA is 

Choose an option

Show full solutionCorrect option: C
Correct answer
C symmetric

Step-by-step explanation

A square matrix P is said to be a symmetric matrix, if PT=P and it is said to be a skew symmetric matrix, if PT=-P.

Given AT=A, BT=-B

Now, AB-BAT=ABT-BAT

                    =BTAT-ATBT

                    =(-B)A-A(-B)

                    =AB-BA

⇒AB-BA is a symmetric matrix.

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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.