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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)

best_answer

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

 

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