Here, A has a greater atomic number than B, which has a greater atomic number than C. To assign E,Z designations you would divide the double bond into left and right portions and assign priorities. On the right side, A > C. However, on the left side, B = B. A (first priority on right side) is simultaneously on the same side and on opposite sides to B (first priority on left side). How would you class this compound then?
When both the substituents are identical on one side of the double bond, the compound does not show geometrical isomerism.
There is no point in using E-Z nomenclature in that case.