so which means is closed under addition.b) Show that is a subring of
so which means is closed under multiplication.
if has an identity element then for all and and thus
for this part you do need to have define the map by then we also havec) Prove the analogue of Cayley's theorem for by showing that of (b) is isomorphic to
so is a ring homomorphism. to show that it's 1-1, let then for all put to get finally, it's trivial that is onto.