Proof of union of subgroups as a subgroup

[needhelp83]

Prove that if (H,o) and (K,o) are subgroups of a group (G,o), then (H \cap K,o) is a subgroup of (G,o).

Proof:
The identity e of G is in H and K, so e \in H\capK and H\capK is not empty. Assume j,k \in H\capK. Thus jk^{-1} is in H and K, since j and k are in H and K. Therefore, jk^{-1} \in H \cap K making H\capK a subgroup.

Just trying to check this proof and see if I did a a good job at it.

Let (G,o) be an Abelian group and let a,b \in G, Prove that (a o b)^{2}=a^{2} o b^{2}


Not sure where to begin with this proof. Any help?

 

[matness]

The first one is fine
For the second just use definition of ^2
(a*b)^2= (a*b)*(a*b)
and definition of abelian groups i.e cahnging places of elements does not effeect anything

 

[needhelp83]

Thanks for the help matness