Prove: $(a^{-1})^{-1}=a$ Over A Field let $0\neq a\in \mathbb{F}$ 
Prove: $$(a^{-1})^{-1}=a$$
I have tried to start with the definition of an inverse, For all  $0\neq a\in \mathbb{F}$  we have:
$$a\cdot a^{-1}=a^{-1}\cdot a=1$$ But could not find a way to continue (tried multiplying by  $(a^{-1})^{-1}$

$$(a^{-1})^{-1}(a^{-1})=1\implies (a^{-1})^{-1}(a^{-1})a=(a^{-1})^{-1}=a$$
