Áp dụng tính chất dãy tỉ số bằng nhau ta có:
$\frac{x-y-2020}{x}=\frac{y-x-2020}{y}=\frac{-x-y+2020}{2020}=\frac{x-y-2020+y-x-2020-x-y+2020}{x+y+2020}=\frac{-\left( x+y+2020 \right)}{x+y+2020}=-1$$\Rightarrow \left\{ \begin{align}
& x-y-2020=-x \\
& y-x-2020=-y \\
& -x-y+2020=-2020 \\
\end{align} \right.$$\Rightarrow \left\{ \begin{align}
& 2x-y=2020 \\
& 2y-x=2020 \\
& x+y=4040 \\
\end{align} \right.$$\Rightarrow x=y=2020$
Khi đó $A=\left( 2-\frac{y}{x} \right)\left( 2-\frac{2020}{y} \right)\left( 2-\frac{x}{2020} \right)$$=\left( 2-\frac{2020}{2020} \right)\left( 2-\frac{2020}{2020} \right)\left( 2-\frac{2020}{2020} \right)=1$