Strang course is too verbose and one does not need the whole course to do practical work. Linear algebra done right is the book you need if you want to apply in practice rather than just watching mit videos. https://www.amazon.com/Linear-Algebra-Right-Undergraduate-Ma...
Axler's book is fantastic. But sadly Springer altered the typesetting on the 3rd edition. A really classic and clear LaTeX layout got turned into something much less clear. This freaked me out. Look inside and compare:
* Second edition: https://www.amazon.com/dp/0387982582
* Third edition: https://www.amazon.com/dp/3319307657
I wonder whether widespread adoption of his book pushed editors to make it look flashier and watered down. The contents are the same though.