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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. $1$ is an eigenvalue of $A$

2. The magnitude of any eigenvalue of $A$ is at most $1$

3. Eigenvalue of $A$ can be negative

Then which of the following is 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