Consider the group G = {1, −1, i, −i, j, −j, k, −k} under
multiplication. Here
i2= j2= k2= ijk = −1. determine which of the following sets is a
subgroup
of G. If a set is not a subgroup, give one reason why it is
not.
(a) {1, −1}
(b) {i, −i, j, −j}
(c) {1, −1, i, −i}
(d) {1, i, −i, j}