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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.

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

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

Solution

Statement-1 is true because the product of symmetric matrices is symmetric under certain conditions, and both A(BA) and (AB)A maintain symmetry. Statement-2 is also true since if A and B commute, their product AB is symmetric, but it does not explain the symmetry of the products in Statement-1.

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