A lot of comments about textbooks that helped in specific topics but I don't think that answers the spirit of OP's question. Sure working through ANY Linear Alg

A lot of comments about textbooks that helped in specific topics but I don't think that answers the spirit of OP's question. Sure working through ANY Linear Algebra textbook is going to improve your Linear Algebra skills. In the spirit of OP's question: How to Solve it by G. Polya Solving Mathematical Problems by Terrence Tao Introduction to Mathematical Thinking by Keith Devlin Are all amazing, How to Solve it in particular is an all time classic.