Hello, I have a general question about isomorphisms of vector spaces. I understand the concepts of mappings being one to one, and onto, but how do I go about SHOWING that a mapping is either one to one, onto, one or the other or both? For example, the mapping R^2-->R^2 defined by f(x,y) = (x-2y, x+y). I'm hoping someone can use this simple example to demonstrate how I would go about it. (it's bijective and an isomorphism btw). The textbook we use doesn't show a general method for showing a mapping is 1:1/onto, but rather proves that a mapping ISN'T 1:1 or onto by means of a contradictory example. Thanks in advance!