



 
Hi Jim, A binary operation × on a set A is commutative if for each element a and b in A, a × b = b × a. If there is only one element in A then a = b. Is the condition above true if a = b? For the associate property write the definition and then replace the name of each element by the same letter. Is the condition true? For your last question there are only a few possibilities. If the two elements are a and b then
Try the various combinations and see if each satisfies the associate property. Penny  


Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences. 