This book is an excellent introduction to linear algebra and is the consistent textbook for Massachusetts Institute of Technology's (MIT) linear algebra course 18.06. If you plan to seriously study any of the physical sciences: mathematics, physics,engineering etc. you will do well to master linear algebra. It is one common pervasive theme is all of these subjects. This book will guarantee that mastery and was designed to help students from all of these disciplines. It is quite enjoyable to read and has a very nice set of problems to work.
In 2006 I worked with some students who wanted to truly master this material. During that time I read and worked through all the problems from the book. I also worked many of the Matlab computational exercises.