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Matrices
Question
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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 with B is commutative.

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

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

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

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

Answer

B.

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

A' = A , B' = A
P = A(BA)
P' = (A(BA))'
= (BA)' A'
= (A'B') A'
= (AB) A
= A(BA)
∴A(BA) is symmetric
similarly (AB) A is symmetric
Statement(2) is correct but not correct explanation of statement (1).

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