This is pretty easy. For i), there is no function S, whether linear or not, such that ST = id.
Notice that once you have taken you have lost all information on . There is no way to know what is in order to regain it. A more technical way of saying that is that T is not "one to one". Many different vectors will be mapped into the same .
As for the second problem, the only difficulty is that there are an infinite number of correct answer- just choose one.