Prove using the multiplication axioms that if x is not zero, then 1 / (1/x) is equal to x.

Prove that there is no rational number, p, such that p^2 = 12

I understand the proof for p^2 = 2 by contradiction by showing that it was not reduced to lowest term because both a and b in a/b turned out to be even, but i can't seem to duplicate the process for 12.

Thanks!

I have another question i'm having trouble with.

If K is greater than or equal to 2 and x is an element in R^k space, prove that there exists y in R^k space such that y is not zero but x*y=0

Thanks so much.