Given that, a*b=1+ab → (1) Now, b*a=1+ba=1+ab=a*b ⇒a*b=b * a Thus, * is commutative. Now, (a*b)*c=(1+ab)*c =1+(1+ab)c=1+c+abc But, a*(b*c)=a*(1+bc) =1+a(1+bc)=1+a+abc So, (a*b)*c≠a*(b*c) Thus, * is not associative. Hence, * is commutative but not associative.