Question 66
Does there exist an operation $*$ on the set of all integers such that the following conditions hold simultaneously:
(1) for any integers $x$, $y$, $z$, $(x * y) * z = x * (y * z)$;
(2) for any integers $x$ and $y$, $x * x * y = y * x * x = y$?
(1) for any integers $x$, $y$, $z$, $(x * y) * z = x * (y * z)$;
(2) for any integers $x$ and $y$, $x * x * y = y * x * x = y$?