Hello

. Need some fast help on this:

Let

G, \star)\rightarrow(H, \triangle) " alt="\phi

G, \star)\rightarrow(H, \triangle) " /> be an isomorphism between these two groups. If

is the inverse element of

, then prove that

is the inverse element of

.

I tried like this:

Since

is isomorphism, that means it is a one to one map thus

only when

and since

is isomorphism,

must be the inverse of

.

I can't see any explanation or justification here...in fact, the argument is true for ANY group homomorphism, isomorphism or not, and the proof is boringly simple: Tonio
Do you think my prove is enough, if not please elaborate.

Thanks for your time.