Why is this matrix invertible? I'm following Intro to stochastic processes by Lawler, page 27. 
It says if we have a matrix Q such that $Q^n \rightarrow0$, then the eigenvalues of Q have absolute value less than $1$. That part I understand.
Then it says: "Hence, $I-Q$ is invertible." How does that follow?
P.S. I understand the conditions for invertibility, like det can't be zero etc.

Following through on a hint given in another answer:
Assume that zero is an eigenvalue of $I-Q.$  Then $(I-Q)\mathbf{x}= \mathbf{0}$ for some $\mathbf{x}$.  So $Q\mathbf{x}=\mathbf{x}$ and $\lambda=1$ is an eigenvalue of $Q$, contradicting $|\lambda|<1$.
We also know that the product of the eigenvalues of a matrix equals its determinant.  So, since the eigenvalues of $I-Q$ are all non-zero, their product is non-zero, thus $\det(I-Q)\ne0$, and $I-Q$ is invertible.
