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The axial symmetry is clear form the matrix of V. the matrix is M = diag(-1,-1, 2) so if you proform a rotation around the z axis, M’ = O M O^-1 , you will find that M’ = M. Then can be sen because the 2×2 x, y block of the matrix is just equal to -1 times the unity matrix.
Another way to this is by looking at the picture of the model. The e- chrarges ar both located on the z axis so the setup is invariant under a rotation around the z axis.
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