VTRMC 1980 Problem 1

Let $*$ denote a binary operation on a set $S$ with the property that $$(w*x)*(y*z) = w * z$$ for all $w,x,y,z\in S.$ Show

(a) If $a*b=c,$ then $c*c = c.$ (b) If $a*b=c,$ then $a*x=c*x$ for all $x\in S.$