Solved: Prove |HK|=|H||K| When H, K are Subgroups of G and H\capK = <e>

[chycachrrycol]

So the problem is if H and K are subgroups of G with HK = {hk \in G| h \in H, k \in K}. If we know that H\capK = <e>, show |HK|= |H||K|

My work so far:
h, j \in H
k,l \in K
i know that if hk = jl then j^{-1}h = lk^{-1}
But I'm not sure what to do from here.

 

[Dick]

j^(-1)h belongs to H, right? What about lk^(-1)?