Let A and B be two symmetric matrices of order 3 .

Statement -1 : A(BA) and (AB)A  are symmetric matrices.

Statement -2 : AB  is symmetric matrix if matrix multiplication of A and B is commutative.

  • Option 1)

    Statement-1 is true, Statement-2 is false.

  • Option 2)

    Statement-1 is false, Statement-2 is true.

  • Option 3)

    Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1 .

  • Option 4)

    Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.

 

Answers (2)

As we learnt in 

Property of Transpose Conjugate -

\left ( AB \right )^{\Theta }=B^{\Theta } A^{\Theta }

- wherein

A^{\Theta } is the conjugate matrix of A

 

 Given that A^{T}=A\, \, \, and\, \, \,B^{T}=B

Then \left [ A\left ( BA\right ) \right ]^{T}= \left ( BA \right )^{T}A^{T}= A^{T}B^{T}A^{T}= ABA

Similarly \left [\left ( AB\right )A \right ]^{T}=ABA

AB is symmmetric matrix.

If AB is commulative.


Option 1)

Statement-1 is true, Statement-2 is false.

Incorrect Option

 

Option 2)

Statement-1 is false, Statement-2 is true.

Incorrect Option

 

Option 3)

Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1 .

Incorrect Option

 

Option 4)

Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.

Correct Option

 

N neha

Preparation Products

Knockout JEE Main April 2021

An exhaustive E-learning program for the complete preparation of JEE Main..

₹ 22999/- ₹ 14999/-
Buy Now
Knockout JEE Main April 2022

An exhaustive E-learning program for the complete preparation of JEE Main..

₹ 34999/- ₹ 24999/-
Buy Now
Test Series JEE Main April 2021

Take chapter-wise, subject-wise and Complete syllabus mock tests and get in depth analysis of your test..

₹ 6999/- ₹ 4999/-
Buy Now
JEE Main Rank Booster 2021

This course will help student to be better prepared and study in the right direction for JEE Main..

₹ 13999/- ₹ 9999/-
Buy Now
Test Series JEE Main April 2022

Take chapter-wise, subject-wise and Complete syllabus mock tests and get an in-depth analysis of your test..

₹ 6999/-
Buy Now
Boost your Preparation for JEE Main 2021 with Personlized Coaching
 
Exams
Articles
Questions