In the following, is the subset H a subgroup of the given

Last updated: 8/9/2022

In the following, is the subset H a subgroup of the given group G? (a) G = Z6, H = {[0], [2], [4]} (b) G = S4, H = {e, (1 2 3), (2 4)(1 3), (1 3 2 4), (1 3)} (c) G = Gl₂ (R), Remember that Gl₂ (R) is the group of invertible matrices (non-zero determinant) with the group operation being matrix multiplication.