What is the 'formal' inverse of a matrix?

Question

I know what 'formal' usually means in a mathematical context, as in a formal proof or definition but I've never heard it being used to describe matrices. I couldn't find any explanation of this online. Any help would be much appreciated.

Answer 1

In algebra, formal means using letters, without any care whatsoever about whether or not what you are writing actually makes sense when you replace the letters with some actual numbers, or functions, .

Example: the formal inverse of $1-X$ is $1+X+X^2+X^3+...$, no matter what $X$ is.