1. Statement A:
   • Claim: The identity of a subgroup is the same as that of the group.
   • Verification: By definition, a subgroup H of a group G must share the same identity element e. This is required for closure under the group operation and inverses.
   • Conclusion: Correct
2. Statement B:
   • Claim: The inverse of any element in the subgroup is the same as its inverse in the group.
   • Verification: In a subgroup H, for any h ∈ H, the inverse h⁻¹ must satisfy h · h⁻¹ = e. Since H inherits the group operation from G, the inverse in H is identical to the inverse in G.
   • Conclusion: Correct 
3. Statement C:
   • Claim: The order of an element in the subgroup matches its order in the group.
   • Verification: The order of an element h is the smallest positive integer n such that hⁿ = e. This property depends only on the element and the group operation, which are unchanged in the subgroup.
   • Conclusion: Correct 
4. Statement D (All of the above):
   • Since A, B, and C are all valid, D is the correct choice.

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