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The Eigen values of $A=\begin{bmatrix} a& 1& 0\\1 &a &1 \\0 &1 &a \end{bmatrix}$ are______

  1. $a,a,a$
  2. $0,a,2a$
  3. $-a,2a,2a$
  4. $a,a+\sqrt{2},a-\sqrt{2}$
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Plz see the picture below for detailed answer.

1. Using properties to eliminate options:

2. Using general procedure: 

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