Prove Vector Space Properties Using Vector Space Axioms

Using the axiom of a vector space, prove the following properties.
Let V$V$ be a vector space over R$\mathbb{R}$. Let u,v,w∈V$u,v,w\in V$.

(a) If u+v=u+w$u+v=u+w$, then v=w$v=w$.

(b) If v+u=w+u$v+u=w+u$, then v=w$v=w$.

(c) The zero vector 0$\mathbf{0}$ is unique.

(d) For each v∈V$v\in V$, the additive inverse −v$-v$ is unique.

(e) 0v=0$0v=\mathbf{0}$ for every v∈V$v\in V$, where 0∈R$0\in \mathbb{R}$ is the zero scalar.

(f) a0=0$a\mathbf{0}=\mathbf{0}$ for every scalar a$a$.

(g) If av=0$av=\mathbf{0}$, then a=0$a=0$ or v=0$v=\mathbf{0}$.

(h) (−1)v=−v$(-1)v=-v$.

The first two properties are called the cancellation law.