For real numbers $a$ and $b$, define $a\textdollar b = (a - b)^2$. What is $(x - y)^2\textdollar(y - x)^2$?
$\textbf{(A)}\ 0 \qquad \textbf{(B)}\ x^2 + y^2 \qquad \textbf{(C)}\ 2x^2 \qquad \textbf{(D)}\ 2y^2 \qquad \textbf{(E)}\ 4xy$
$\left[ (x-y)^2 - (y-x)^2 \right]^2$
$\left[ (x-y)^2 - (x-y)^2 \right]^2$
$[0]^2$
$0 \Rightarrow \textbf{(A)}$