Define multiplication on ?? by ? ? ? = ? where ? is theremainder when the product ?? is divided by ?.
(a) Show that this operation is commutative.
(b) Show that this operation is associative.
(c) Show that there is an identity element for thisoperation.
(d) Show that for ? = 5, the set of non-zero elements forms agroup under multiplication.
(e) Show that for ? = 6, the set of non-zero elements does notform under multiplication.
