Divisibility question: If $m=a_1x+b_1y$, $n=a_2x+b_2y$ and $a_1b_2-a_2b_1=1$, then prove that $\mathrm{GCD}(m,n)=\mathrm{GCD}(x,y)$
If $(k,l) = 1$, show that $(b_2k-b_1l, a_1l-a_2k) = 1$ for $a_1b_2-a_2b_1=1$