Let $R$ be any ring. Prove that the following equations must hold in $R$.

By letting $R$ be any ring I have to show these following equations hold in $R$:

a) $x\cdot 0=0$

b) $0\cdot x=0$

c) $-(-x)=x$

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 $R$.

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