For injective, you need to say that is not equal to (you start with , but then you concluded that but not that ).
So, a proof would be: Note that for , but .
What you did was write down the working to find the proof, but it wasn't the proof itself per se.
For surjective, you start with something arbitrary in the image, A, and find something which maps to it. So, let . Can you think of some such that ?