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 a symmetric matrix if matrix multiplication of A and B is commutative.

Given, A = AT and B = BT
Now (A(BA))T = (BA)TAT = (BA)A = A(BA)
Similarly ((AB)A)T = (AB)AT = (AB)A
So, A(BA) and (AB)A are symmetric matrices.
Again (AB)T = BTAT
Now if BTAT = AB, then AB is a symmetric matrix.
Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
Hence, option 'D' is correct.