Let be sets and let and be functions.
(1) Suppose is an injective map from to itself. Show that is injective.
(2) Suppose now that and . Show that is bijective and .
(1) is 1-1 such that ,
It follows that . Is this proof correct? Do I need to add any more explanation?
(2) I need some help with question two, so I can get started. Btw, the and notation represents the identity.
Thanks in advance,