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.

Engineering

Mathematics

Symmetric and Skew Symmetric Matrices

Question

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 and Statement-2 is the correct explanation of Statement-1.

Statement-1 is true, Statement-2 is false and Statement-2 is not the correct explanation of Statement-1

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

Statement-1 is true, Statement-2 is false

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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).