I've not ever heard of either of those books, but I've taught linear algebra before and my advice is to buy (or borrow or rent or whatever) the book your instructor assigned.
- Homework is often assigned out of the book so you need access to the class text anyway.
- Most linear algebra books cover pretty much the exact same stuff so the advantage of having the book you want over the book that was assigned is probably minimal.
- Though the material is the same, the order is definitely not always the same. If the book you want covers the material in a different order then you're gonna have a hard time understanding proofs that rely on material that you haven't gotten to in class but the book assumes you understand.
- Professors sometimes (though not always) know the book they are teaching out of very well and tailor their class presentation to complement whats in the book. You'll be missing out on that.
There are certainly obvious counter arguments to some of what I've said, but I don't think they add up to the weight of the possible downsides.
That said, point (2) and the fact that you already have the other book might convince you to try and not get the class text. If you're gonna go that route just ask the professor why it is/isn't a good idea. If he has reasons to say you shouldn't they're probably honest reasons and he'll probably tell you them straight out. You should also look at the table of contents of the two books and see if you can spot anything that's obviously out of order. That will clue you in to where the potential future pitfalls of your decision might come. Check both books against a class syllabus too (if there's one detailed enough to list topics and/or a schedule).