Consider an $n \times n$ matrix $A$ with the property that each element of $A$ is non-negative and the sum of elements of each row is $1$.
Consider the following statements.
- $1$ is an eigenvalue of $A$
- The magnitude of any eigenvalue of $A$ is at most $1$
- Eigenvalue of $A$ can be negative
Then which of the following is $\text{TRUE?}$
- Only statement $1$ is correct
- Only statements $1$ and $2$ are correct
- Only statements $1$ and $3$ are correct
- Only statements $2$ and $3$ are correct
- All statements $1,2$ , and $3$ are correct