Linear Algebra Done Right by Sheldon Axler is indeed a good book if you are look...

Linear Algebra Done Right by Sheldon Axler is indeed a good book if you are looking for a rigorous proof based book to learn linear algebra.

Here [1] you can find Sheldon Axler himself explaining the topics of the book in his YouTube channel! How wonderful is that!

Here [2] you can find the solutions to the exercises in the book.

This [3] Lectures might help as well, among the books this course follow is Algebra Done Right.

Good luck learning the subject of Linear Algebra you'll have fun doing so.