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TIFR ECE 2023 | Question-9

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 ?

  1. Only statement $1$ is correct
  2. Only statements $1$ and $2$ are correct
  3. Only statements $1$ and $3$ are correct
  4. Only statements $2$ and $3$ are correct
  5. All statements $1,2$ , and $3$ are correct


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