Another way of proving option C
For Groups we know cancellation property holds, i.e.
a.b=a.c ⇒ b=c (why this is true ?, because we have inverse element for each group. see this)
Having known this,
(goh)^{2}=(goh)o(goh) = gohogoh (im removing bracket because groups are associative ).
Now LHS becomes gohogoh. and RHS is g^{2}oh^{2}. We want to proof gohogoh = g^{2}oh^{2}.
gohogoh = g^{2}oh^{2}
⇒g̶ohogoh =g^{2̶}oh^{2} (cancel leftmost g from each sides, then it becomes hogoh = goh^{2})
Similarly, cancel rightmost h from both sides. then it becomes hog = goh.
which is true for abelian groups, since abelian groups are commutative.