>I'm not sure that Axler's book is great as a first LA book.

Linear Algebra Done Right is a text for beginners who want to study linear algebra in a proof based, mathematically rigorous way.

So, if you want that I think it's a good fit as a first linear algebra book.

From "Preface to Students":

> You are probably about to begin your second exposure to linear algebra. Unlike your first brush with the subject, which probably emphasized Euclidean spaces and matrices, this encounter will focus on abstract vector spaces and linear maps. These terms will be defined later, so don’t worry if you do not know what they mean. This book starts from the beginning of the subject, assuming no knowledge of linear algebra. The key point is that you are about to immerse yourself in serious mathematics, with an emphasis on attaining a deep understanding of the definitions, theorems, and proofs.

It is definitely a hard text if you haven't had exposure to linear algebra before.

The thing is, by the time you get to this book, most students have probably taken DiffEq or multivariable calculus, and had exposure to linear algebra there. (If not in high school.)

That was my path and that first introduction was awful. Axler made everything finally make sense to me.