# Math Help - How do you prove these statements?

1. ## 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.

2. 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.