Consider the 5 5 matrix text A = left begin array...

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Consider the 5 × 5 matrix \[{\text{A}} = \left[ {\begin{array}{*{20}{c}} 1&2&3&4&5 \\ 5&1&2&3&4 \\ 4&5&1&2&3 \\ 3&4&5&1&2 \\ 2&3&4&5&1 \end{array}} \right]\]
It is given that A has only one real eigen value.
Then the real eigen value of A is

A. -2.5

B. 0

C. 15

D. 25

Answer: Option C

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