I know that if $\rho(A) < 1$ then $I-A$ is invertible but I am stuck with the opposite direction. So far I have only shown the trivial $\rho(A) \neq 1$. Any hints?
2026-03-26 22:53:43.1774565623
If $I - A$ is invertible, is $\rho(A) < 1$?
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Well, $I-(-I)$ is invertible and $\rho(-I)=1$...