ILL 1977 Problem 31

Let $f$ be a function defined on the set of pairs of nonzero rational numbers whose values are positive real numbers. Suppose that $f$ satisfies the following conditions:(1) $f(ab,c)=f(a,c)f(b,c),\ f(c,ab)=f(c,a)f(c,b);$ (2) $f(a,1-a)=1$ Prove that $f(a,a)=f(a,-a)=1,f(a,b)f(b,a)=1$ .