A′=A,B=B′=B given as both A and B are symmetric. Let us choose that A and B are symmetric. Let us choose that A and B commute
i.e., AB=BA
AB will be symmetric if (AB)′=AB
Now (AB)′=B′A′=BA=AB by (1)
∴ AB is symmetric
Converse: Choose that AB is symmetric.
∴ (AB)′=AB or B′A′=BA=AB or BA=AB
∴ A and B commute.