I think I'm confused about notation perhaps.

let

be a homomorphism

define

for h,k in G

give a necessary and sufficient condition for it to be a homomorphism... prove why.

i know to show something is a homomorphism i have to show that

, ie. that the binary operation's action is preserved in both groups. but i don't know how to here. for a=(m,n) and b=(i,j), is ab=(mi,nj)? that would give

. How do I go about setting conditions to make these equal...? Seems to me they only would be if h,k were 0 or 1?