Lots of matrices don't have an inverse.
Skill in Algebra
HN: Introduction to Applied Linear Algebra: Vectors, Matrices, and Least Squares (2018)
Immersive Linear Algebra (HN)
Relearning Matrices as Linear Functions (HN)
Thirty-three Miniatures: Mathematical and Algorithmic Applications of Linear Algebra (HN)
A Brief Guide to A Few Algebraic Structures