Question 3
a) Show that the multiplicative inverse of a unit in a ring with unity is unique
b) Show that a^2 - b^2 = (a + b)(a - b) for all a,b in a ring R if and only if R is commutative
c). Show that the intersection of subrings of a ring R is again a subring of R
d). Showing all your working, solve the equation 3x = 2 in Z7
e). An element a E R in a ring R is idempotent if a^2 = a. Hence
i). show that the set of all idempotent elements of a commutative ring is closed under multiplication
ii). find idempotent elements in Z6