Q on associative binary operation

[BillyGOTO]

On Thu, Aug 28, 2003 at 12:14:20AM -0700, Sarad AV wrote:
> hi,
> 
> Table shown is completed to define 'associative'
> binary operation * on S={a,b,c,d}. 
> 
> *|a|b|c|d
> ---------
> a|a|b|c|d
> ---------
> b|b|a|c|d
> ---------
> c|c|d|c|d
> ---------
> d|d|c|c|d
> 
> 
> The operation * is associative iff (a*b)*c=a*(b*c) for
> all a,b,c element of set S.

> So can (a*d)*d=a*(d*d)=d considered as associative
> over * for this case as per definition?

a   d       d   d
 \ /         \ /
  d   d   a   d
   \ /     \ /
    d   =   d

What's the problem?