Usage of ring axioms.

Question

I have 3 questions which have to be answered through the application of the ring axioms. Let $R$ be a ring and show that:

a) $-0 = 0$. For this one you can assume that $(R,+)$ is a group and hence the identity is $0$, meaning $-0 + 0 = 0 + 0 = 0$. Is this correct?

b) $(-1)a = -a$ for all $a\in R$

c) $(-1)(-1) = 1$

(For b and c let $R$ be a ring with identity $1$).

I am not sure where to proceed for b) and c) and so any help to push me in the right direction would be greatly appreciated!

Answer 1

For b), prove that $(-1)a+a=0$.

For c), use b).