What is a good book to study linear algebra?

"Linear Algebra Done Right" by Sheldon Axler is an excellent book.

Gilbert Strang has a ton of resources on his webpage, most of which are quite good:

http://www-math.mit.edu/~gs/

Well, I will just add a few online resources that I have used before,

William Chen's Lecture Notes
Jim Hefferon's Linear Algebra
Edwin Connell's Linear Algebra
Keith Matthew's Linear Algebra
Keith Matthew's Lecture Notes on some advanced linear algebra
Ruslan Sharipov's Course of linear algebra and multidimensional geometry

My favorite textbook on the subject by far is Friedberg,Insel and Spence's Linear Algebra, 4th edition. It is very balanced with many applications,including some not found in most LA books,such as applications to stochastic matrices and the matrix exponetioal function,while still giving a comprehensive and rigorous presentation of the theory.It also has many,many exercises-all of which develop both aspects of the subject further. This is without question my favorite all purpose LA book for the serious mathematics student.

Why do we define quotient groups for normal subgroups only?

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Multiples of an irrational number forming a dense subset

Density of sum of two independent uniform random variables on $[0,1]$

How do you show monotonicity of the $\ell^p$ norms?

Proving that a doubly-periodic entire function $f$ is constant.