Hi! I have a midterm tomorrow and I am stuck on this problem. Can anyone help me??? Thankkk youu soo much.

1) Suppose F is a field, andais a nonzero element of F. Show that if r, s are in F and ar = as, then r = s.

2) Let R be a ring with identity. Prove that for all a, b, c in R, if a + b = 0 and a + c = 0 then b = c. (This means that for any a in R, the element -a is uniquely determined.