Let $A$ be an $n \times n$ matrix.
i) Prove that if the sum of each row of $A$ equals $s$, then $s$ is an eigenvalue of $A$.
ii) Prove that if the sum of each column of $A$ equals $s$, then $s$ is an eigenvalue of $A$.
The first question isn't a problem, but I've been banging my head against the wall for an hour trying to find the answer to the second one. I'd really appreciate some help.
Best Answer
Per the comment above: the key is to note that $A$ and $A^T$ have the same eigenvalues.