# Let A and B be two symmetric matrices of order 3. [2011] 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.

Question:

Let $A$ and $B$ be two symmetric matrices of order 3.

Statement-1: $A(B A)$ and $(A B) A$ are symmetric matrices.

Statement-2: $A B$ is symmetric matrix ifmatrix 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 Option: 1

JEE Main Previous Year 1 Question of JEE Main from Mathematics Inverse Trigonometric Functions chapter.
JEE Main Previous Year 2011

Solution:

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