I'm stuck on a problem where I need to find a counterexample. I'm not sure how to come up with a reducible matrix to show that it doesn't satisfy the result of the following corollary. Any solutions, hints, or suggestions would be appreciated.
Show by an example that the hypothesis of irreducibility in (6.2.28) is necessary.
Think simple. For example, $$ \pmatrix{1&0\\0&0} $$