By letting $R$ be any ring I have to show these following equations hold in $R$:
a) $x\cdot 0=0$
b) $0\cdot x=0$
d) $(-x)\cdot(-y)=x\cdot y$
I'm not really looking for the answer just for a hint to get me started. I guess I'm confused on how to show these properties hold within $R$.