TIFR ECE 2023 | Question: 9

Question

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 $\text{TRUE?}$

• A. Only statement $1$ is correct
• B. Only statements $1$ and $2$ are correct
• C. Only statements $1$ and $3$ are correct
• D. Only statements $2$ and $3$ are correct
• E. All statements $1,2$ , and $3$ are correct