It's very easy to determine your dominant eye with a 10 seconds test.

1 Look at a object about 3 - 4 meters distance from you.
2 Stretch your right arm (or left arm if you're left handed) and point to the object with your forefinger.
3 Close your left eye: are you still pointing to the object or slightly next to it with your right eye?
If you're still pointing to the object, your right eye is your dominant eye, if you're pointing slighty next to the object it means it is not your dominant eye.
4 Now close your other eye and repeat step 3.
5 In rare cases one doesn't have a dominant eye.