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Consider  the 5 $\times$ 5 matrix

$$\begin{bmatrix} 1&2&3&4&5\\ 5&1 &2& 3 &4\\ 4&5&1&2&3\\ 3&4&5&1&2\\ 2&3&4&5&1 \end{bmatrix}$$

It is given that A has only one real eigenvalue. Then the real eigenvalue of A is

  1. $-2.5$
  2. $0$
  3. $15$
  4. $25$
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