The identity element of any structure operated on multiplication is 1.
ie, $x*1=x$
But if you have 0 in your set, then
0 multiplied by what = 1? There's no answer to that.
So, having 0 in your set, if it is defined under multiplication would fail to have an inverse.
No inverse => Not a group => Not Abelian.
Option C
Why is D True? Because it excludes 0.
Why are A and B True? Because they're defined on addition. Means their identity is 0.
ie, $x+0=x$
They'll have closure, associativity, identity, inverse and commutativity.