Linear Algebra is not what it seems at first thought. Behind all the matrices, polynomials, vectors and spaces, there is a fascinating subject which tools can help you to solve many practical problems. Linear Algebra is a topic connected to different fields inside and outside mathematics like functional analysis, differential equations, engineering, graph theory, statistics, linear programming, and computer graphics.
There are hundreds of books with the aim of teaching Linear Algebra, your choice will depend, basically, on the kind of course you are taking, and on the approach, prose and rigor of the text you prefer to study. Here I propose a brief list of books, based on my personal experience, from famous books I have read or consulted.