If $a,b,c$ are the roots of $x^3-px+q=0$, then what is the determinant of the given matrix in $a, b, c$? 
If $a,b,c$ are the roots of $x^3-px+q=0$, then what is the determinant of 
  $$
    \begin{pmatrix}
    a & b & c \\
    b & c & a \\
    c & a & b \\
    \end{pmatrix} \,\,?
$$
  (A) $p^2+6q \quad$
  (B) $1 \quad$
  (C) $p \quad$
  (D) $0 \quad$

In this equation given we have product of eigenvalues given as $-q$ and we know product of eigenvalues is determinant then why isn't the determinant is $-q$?  

$$\det\begin{pmatrix}a&b&c\\ b&c&a \\ c&a&b\end{pmatrix}=(a+b+c)\det\begin{pmatrix}1&1&1\\ b&c&a \\ c&a&b\end{pmatrix}=0$$
since $a+b+c=0$.
