I'm not a math guy at all, however, I am a google guy.

Googled around a bit, and found:

http://mathworld.wolfram.com/Eigenvalue.html

Just from reading your book, and some google pages, I'd say "Yes" to using non matrix rules to subtract terms. To me (not an expert, just a second opinion) it looks like you're going from matrices, to an equation, then back to a matrix.