Consider the ring R = {0,2,4,6,8,10,12} with the operations being addition and multiplication mod 14.

(a) Show that R is a ring with identity by ﬁnding the multiplicative identity (and prove that it’s the identity by computation).

(b) Find the multiplicative inverse of 10 in R.

Would I be doing this correctly:

For part (a):

8 would be the multiplicative identity since every element in R multiplied by 8 equals itself (mod 14)?