I think, now is the time I should move on to do different area of mathematics. I have done real analysis and topology from Baby Rudin and James Munkres, respectively. I’m thinking to do linear algebra. I’m looking for “standard text” in linear algebra. By standard text, I mean standard text in real analysis is Baby Rudin, Tom Apostol, etc, and in topology Munkres, Dugundji etc. I have seen linear algebra done right by Axler and linear algebra by Hoffman book. IMO those book is basic to my taste. Dugundji is an amazing topology book. Is there an equivalent book in linear algebra? By equivalent I mean, in terms of rigorousness and exercise/problem in textbook.
Edit: I read almost all linear algebra book recommended by SE users. One thing is common in those books are examples and computational problems. There are lots & lots of examples(in the order of 10 in each section). Some examples involve concepts of number theory, matrix, etc. which I have never studied. I guess, I’m looking for a book which don’t contain crazy amount of examples.
The 2022 standard text for basic Linear Algebra is Gilbert Strang's Linear Algebra. It is used in a more or less direct way in every university I have ever been, and should be in every Mathematical Library which respects itself.
I would suggest you start there and there see where you should focus. It starts from ground zero, so I guess you could also replenish any shortcomings you may have acquired over your studies.