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Math Help - How do you prove these statements?

  1. #1
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    How do you prove these statements?

    Prove these using only field axioms, order axioms and the fact that 1>0 and x0=0
    a. (a^-1)^-1=a
    b. a>0 iff a^-1>0
    c. (ab)^-1=a^(-1)b^(-1)
    d. a>1 iff 0<a^-1<1

    Any help would be great.. Or just a push in the general direction, I'm not sure where to start with them, I've done similar ones but I can't seem to see any relations.
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  2. #2
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    First look here Group (mathematics) - Wikipedia, the free encyclopedia.

    Closure
    For all a, b in G, the result of the operation a b is also in G.b[]
    Associativity
    For all a, b and c in G, the equation (a b) c = a (b c) holds.
    Identity element
    There exists an element e in G, such that for all elements a in G, the equation e a = a e = a holds.
    Inverse element
    For each a in G, there exists an element b in G such that a b = b a = e, where e is the identity element.
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