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Demonoid

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**URGENT Field Proofs help.**

I need to prove the following:

1) Prove that if x, y are elements of a field, and X x Y = 0 then either x = 0 or y = 0 .

Write a detailed solution. and mention which of the eld axioms you are using.

2) Let F be a field in which 1 + 1 = 0 . Prove that for any x ∈ F , x = -x

I don't understand how to approach these proofs, since they are so obvious:

1) x times y = 0, of course it will be either x = 0 or y =0, since anything times 0 is 0, but how to go about proving this, I am stuck

2) 1+1=0 => just bring 1 to the right side 1=-1 then for any x=-x. But I don't think this any good of a proof.

I really need some help here, thanks !

---sdfx . drewd