Non-empty subsets of a group

Question

Question:

Non-Empty Subsets of a Group

Let G be a group and H be a non-empty subset of G. We define H² as the set of elements of G which can be written in the form h_1 h_2, with h_1 ,h_2∈H.

Let H be finite. Prove that H is a subgroup if and only if H²=H.