First of all, I know that there are many posts around this topic, but my question, as you will see, has important differences.
I am in the last year of my undergraduate studies, and I have been taught introductive courses of Group Theory, and Ring Theory. Now, I want to attend Galois Theory, but I see that I have no good knowledge of Linear Algebra. So, I thought that this is a good chance to refresh and complete my knowledge. And I look for a good book with many exercises to solve.
In other words, I'm looking for a good Linear Algebra book, which will have all the necessary chapters with exercises and will be useful for Galois Theory, Algebraic Geometry, Representation Theory, Coding Theory and other more advanced algebra courses.
What are your recommendations?
PS1: I didn't like Gilbert Strang's book "Linear Algebra and Its Applications".
PS2: What's your opinion for the books: 1) Linear Algebra, Serge Lang, 2) Introduction to Linear Algebra, Serge Lang and more generally your opinion about Lang's books, 3) Linear Algebra: Step by Step, Kuldeep Singh?
PS3: I apologize for my English!
Thank you in advance!