Just think for a moment about the first part. You don't even have to leave the natural numbers. What is 6*4 and what is 8*3? What does that say about * being 1 to 1? As for onto, try to think of a single real number that is not the product of two real numbers, What is 1*x for any x at all?
These sound like the kind of questions that some books put in to make you think so that you can check if you grasp the concept that the author is trying to explain. You are not helping yourself if you do not try to work this kind of question out for yourself. It is better to get this kind of question wrong after trying it for yourself than just to turn to a forum without trying for yourself first. After all, suppose I had answered Yes, No to your questions how would you know whether my answer could be trusted?
Sorry if this is a harsh response to your first post - but I think you will often get more from the forum if you use it as a way of learning about interesting questions than a way to learn an answer.