It appears that your straight forward request has been ignored 'til now... apologies...
Carrot cake can be as intricate as you'd like, or very simple... here's a quick, simple recipe from our house here in the western U.S. to yours:
1 cup Mayonnaise (or sals dressing)
1 pkg Yellow Cake Mix
4 Eggs
2 1/2 tsp Cinnamon
2 cups finely grated Carrots
Directions
Beat Mayo, Cake Mix, Eggs, 1/4 cup Water and Cinnamon in a bowl.
Stir in Carrots
Pour into a greased 13x9 pan
Bake for 30-35 minutes (350 Fahrenheit ( I said we were in the U.S.))
Cool Before frosting with Cream Cheese Frosting
Best of luck!