If ω is a non-real cube root of unity, then what is a root of the following equation?$ \begin{vmatrix} x+1 & \omega & \omega^2 \\ \omega & x+\omega^2 & 1 \\ \omega^2 & 1 & x+\omega \end{vmatrix} = 0 $

Consider the following in respect of a non-singular matrix M:

I. ∣M²∣=∣M∣²

II. $|M|=|M{}^{-1}|$

III. $|M|=|M{}^T|$

How many of the above are correct?