All of Chapter 5.1 is important. Notice how you get a series of results from the axioms that are almost impossible to even verify if you just computed everything.

Chapter 5.2 should be seen as an application of Chapter 5.1. We will not be using Cramer’s rule or the inverse formula for any computation, but understanding how they come about naturally from the axioms in the beginning of Chapter 5.1 is important. The how, not the formula.

You should be comfortable handling determinants. Every now and then, we will phrase results compactly using determinants. In the section on Eigenvalues, determinants translate the realm of linear algebra to the realm of solving polynomial equations.