Question

Does the composition table:

*	a	b	c
a	b	c	a
b	c	a	b
c	a	b	c

Give a commutative binary operation on the set $\{a, b, c\}$ ?

Answer 1

SOLUTION : $a^* a=b, a{ }^* b=c, a{ }^* c=a, b{ }^* a=c, b{ }^* b=a, b{ }^* c=b, c * a=a, c * b=b, c{ }^* c=c$