Let \(A\) be \(n\times n\) real valued square symmetric matrix of rank 2 with…

Let $A$ be $n\times n$ real valued square symmetric matrix of rank 2 with $\sum_{i=1}^{n}\sum_{j=1}^{n}A^{2}_{ij} = 50.$. Consider the following statements.

I.    One eigenvalue must be in [−5,5]

II.    The eigenvalue with the largest magnitude must be strictly greater than 5

Which of the above statements about eigenvalues of $A$ is/are necessarily CORRECT?