Orthogonal Matrix

Q.

If $A$ and $B$ are two symmetric matrices of order $3$.

Statement I $A\left(BA\right)$ and $\left(AB\right)A$ are symmetric matrices.

Statement II $AB$ is a symmetric matrix If matrix multiplication of $A$ and $B$ is commutative.

1. Statement I is correct, Statement II is correct; Statement II is not a correct explanation for the statement I

2. Statement I is correct, Statement II is incorrect

3. Statement I is incorrect, Statement II is correct

4. Statement I is correct, Statement II is correct, Statement II is the correct explanation for Statement I

Q. Let $A=\left[\begin{array}{ccc}X& Y& Z\end{array}\right]$ be a $3\times 3$ orthogonal matrix with $X,Y,Z$ as its column vectors. Then $B=X{X}^T+Y{Y}^T$

1. is a symmetric matrix
2. is the $3\times 3$ identity matrix
3. satisfies $B^2=B$
4. satisfies $BZ=O,O$ being the null matrix