let us suppose that there are values $a\_1, a\_2, b\_1, b\_2 \in \mathbb{Z}^+$ such that $gcd(a\_1,b\_1) = 1$ and $gcd(a\_2,b\_2) = 1$

I have to prove 

$a\_1b\_2 = a\_2b\_1 => a\_1 = a\_2$ and $b\_1 = b\_2$.