I have read and reread all the text around this and pondered it for hours. Here is the question verbatim.

*If $A$ is an $n\times n$ matrix and if $b$ is a $n\times 1$ matrix, what conditions would you impose to ensure that the equation $x=Ax+b$ has a unique solution for $x$? Assuming that your conditions are satisfied, find a formula for the solution in terms of an appropriate inverse.*

The published answer is that $I-A$ must be invertible, and, $x=(I-A)^{-1} b$.

I believe I understand the other questions in the first two chapters of this book, and the many implications of matrix invertibility. But the published answer (the equation part) makes no sense to me, either on its own or as an answer to the stated question.