Hey.

Given the field F, Prove:

* For any a, b in F, if a*a=b*b, then a=b or a=-b

* For any a, b in F, if a*a*a = b*b*b, then a=b

Given the field F where 1+1=0, Prove:

* For any a in F, -a=a

* For any a, b in F, a+b=a-b

The proofs have to be supported by the axioms of fields rigorously.

I don't know actually how even start proving it.

Thanks.