I like "Contemporary Linear Algebra" by Howard Anton. It's somewhat newer than Axler's and probably the best undergraduate textbook for someone who is starting to learn linear algebra.
Can someone reccomend me a decent, entry-level Linear Algebra book? I was looking at the latest edition of Strang, but the price tag is a bit too high. I would go straight to Axler's "Linear Algebra Done Right" but I think it will be too hard considering I know next to nothing outside of introductory matrix arithmetic.