Question

If $\left|\begin{array}{ccc}1& x& x^2\\ x& x^2& 1\\ x^2& 1& x\end{array}\right|=3$, then the value of $\left|\begin{array}{ccc}{x}^3-1& 0& x-x^4\\ 0& x-x^4& x^3-1\\ x-x^4& x^3-1& 0\end{array}\right|$ is

Answer 1

Answer: 9

$D_c=D^2=9$
$D_c=\left|\begin{array}{ccc}{x}^3-1& 0& x-x^4\\ 0& x-x^4& x^3-1\\ x-x^4& x^3-1& 0\end{array}\right|$