Question

If \( x \) is a complex root of the equation
\[ \begin{vmatrix} 1 & x & x \\ x & 1 & x \\ x & x & 1 \end{vmatrix} + \begin{vmatrix} 1 - x & 1 & 1 \\ 1 & 1 - x & 1 \\ 1 & 1 & 1 - x \end{vmatrix} = 0, \] then \( x^{2007} + x^{-2007} \) is:

• A. \( 1 \)
• B. \( -1 \)
• C. \( -2 \)
• D. \( 2 \)

Hint:

If \( x \) is a cube root of unity, then it satisfies \( x^3 = -1 \), which helps simplify large exponents.