Let A be be $n \times n $ square matrix whose all diagonal entries are 1. Suppose that sum of the abosolute values of each row is less than equal to 2. With this setting , I am looking for the following question:
Question: Prove that for every eigen value $\lambda$ of A , $0 \leq \lambda \leq 2.$
It is easy to see that $|\lambda| \leq 2.$ But how can I show that $ \lambda \geq 0?$
Thank you in advance.