For each of the following sets, determine whether or not the set is a group under the

Question:

For each of the following sets, determine whether or not the set is a group under the stated binary operation. If so, determine its identity and the inverse of each of its elements. If it is not a group, state the condition(s) of the definition that it violates.
(a) {- 1, 1} under multiplication
(b) {- 1, 1} under addition
(c) {- 1, 0, 1} under addition
(d) [10n|n ∈ Z} under addition
(e) The set of all one-to-one functions g: A → A, where A = {1, 2, 3, 4}, under function composition
(f) {a/2n|a, n ∈ Z, n ≥ 0} under addition