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Let A and B be two symmetric matrices of order 3 . This question has Statement -1 and Statement -2 . Of the four choices given after the statements, choose the one that best describes the two statements. Statement -1 : A ( BA ) and ( AB ) A are symmetric matrices. Statement - 2 : A B is symmetric matrix if matrix multiplication of A and B is commutative.

Options

  1. AStatement -1 is true, Statement -2 is true; Statement -2 is not a correct explanation for Statement -1
  2. BStatement -1 is true, Statement -2 is false.
  3. CStatement -1 is false, Statement- 2 is true.
  4. DStatement -1 is true, Statement -2 is true; Statement -2 is a correct explanation for Statement -1

Correct answer

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

Step-by-step solution

aligned & A^ =A, B^ =B & (A(B A))^ =(B A)^ A^ = (A^ B^ ) A=(A B) A=A(B A) & ((A B) A)^ =A^ (A B)^ =A (B^ A^ )=A(B A)=(A B) A aligned Statement -1 is correct Statement - 2 (A B)^ =B^ A^ =B A=A B ( AB is commutative) Statement -2 is also correct but it is not correct explanation of Statement -1

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