Ask Me Help Desk - Matrix Help

1)Given a circular matrix
$ A=\begin{bmatrix} a& b& c\\ c& a& b\\ b& c& a \end{bmatrix} B=\begin{bmatrix} e& f& g\\ g& e& f\\ f& g& e \end{bmatrix} $

1) Show that C=AB is also a cicular matrix. Write the form of a circular matrix 4x4.

* I have done this part

2) Show the vector $x1= \left[1 1 1 \right ]T$ satisfy the linear equations $A x1 = \Lambda 1 x1$

*This part also has been done

3) For the vector x1 in part 2 find the corresponding value of $\Lambda1$
*I guess this part also have been solved.

Now here is my question, instead of $x1=\left[1 1 1 \right ]T$ now the vector x1 is replace by $x1 = \left [1, -\frac{1}{2}+\frac{\sqrt{}3}{2}j,-\frac{1}{2}-\frac{\sqrt{}3}{2}j \right ]T$

Lets assume the value for x1 is the same for the left and right side.
How do we do part 2 and 3 if we use $x1 = \left [1, -\frac{1}{2}+\frac{\sqrt{}3}{2}j,-\frac{1}{2}-\frac{\sqrt{}3}{2}j \right ]T$ [/QUOTE]