$\begin{bmatrix} a &1 &0 \\ 1& a & 1\\ 0&1 &a \end{bmatrix}$
a can be any number. Let's keep it 1.
$\begin{bmatrix} 1 &1 &0 \\ 1& 1 & 1\\ 0&1 &1 \end{bmatrix}$
Trace = $3$ (Sum of eigenvalues)
Determinant = $-1$ (Product of eigenvalues)
Look at option A:
Sum = $3$
Product = $-1$
This is our answer.