Although it’s not a book, a good series on YouTube is 3Blue1Brown Essence of Linear Algebra. That explains it in a very visual way. That, in addition to Linear Algebra and its applications by Gilbert Strang, would be a strong mix. I would also recommend 3000 solved problems in Linear Algebra by Seymour Lipschutz as a strong foundation in linear algebra requires practice.
It should be noted that the sum of the 3B1B videos is like 2 hours, and that Grant himself says that these videos are for summarizing and providing intuition after you have already taken the course.
Essence of linear algebra is an absolutely wonderful series. It gave me an intuition of the subject in a matter of hours in way years of university didn’t do.
My advice as someone who was in the same position and has just done a year in industry and about to go back and do my final year of CS (UK), is make sure you enjoy yourself and learn how to manage your time as this will help dramatically. Then during this time if you can learn parts of the syllabus, so it's not the first time you hear about it when going into a lecture. Find your niche what interests you, and gets you excited, talk to your lectures about that stuff, that can help later, especially if you get bored or want to go into research. Overall spend time doing side projects, enjoying learning, part taking in clubs and societies and if you find it easy find something to challenge you! If you want to ask me anything more about my experience so far, feel free to send a message (email in bio)
