For [real numbers](https://artofproblemsolving.com/wiki/index.php/Real_number) $a$ and $b$, define $a * b=(a-b)^2$. What is $(x-y)^2*(y-x)^2$?
$\mathrm{(A)}\ 0\qquad\mathrm{(B)}\ x^2+y^2\qquad\mathrm{(C)}\ 2x^2\qquad\mathrm{(D)}\ 2y^2\qquad\mathrm{(E)}\ 4xy$
Since $(-a)^2 = a^2$, it follows that $(x-y)^2 = (y-x)^2$, and 
\[(x-y)^2 * (y-x)^2 = [(x-y)^2 - (y-x)^2]^2 = [(x-y)^2 - (x-y)^2]^2 = 0\ \mathrm{(A)}.\]