Let (R, +, •) be a ring with unity u, and |R| = 8. On R4 = R × R × R × R, define + and • as suggested by Exercise 18. In the ring R4,
(a) How many elements have exactly two nonzero components?
(b) How many elements have all nonzero components?
(c) Is there a unity?
(d) How many units are there if R has four units?