Concrete treatment of fundamental concepts and operations, equivalence, determinants, matrices with polynomial elements, and similarity and congruence. Each chapter has many excellent problems and optional related information. No previous course in abstract algebra required.
It's interesting that this book, published in 1966, states that it is for undergraduates since much of this material would now (in 2010) be more likely to appear in a second course in linear algebra. The author writes clearly and this book is a great source of information beyond the introductory material in a modern linear algebra course. I'm not sure where some of this same material can be found in more recently published books. See also Matrices and Linear Transformations, 2nd ed, by Charles Cullen.