Is it normal for a child to do opposite of what is told to be done?

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At this age, a lot of children tend to throw tantrums and try to asses their independence. That is why many people colloquially call it the terrible twos. It is just a passing phase and it will pass and he grows up.

For now what you can do, is when he throws any tantrum, do not pay attention to him. Also when you ask him to do something give him 2 choices which makes him think he is in control, but are acceptable to you. Such as, you can either eat this small piece of cake now, or you can have a bigger piece after dinner. You can have a chocolate one you have washed your hands. Or, I can allow you a treat only if you promise to brush later. Basically, he will understand small contracts/ promises. A give and take is understandable for him, as compared to doing something so that it is good for him. Also once he starts going into play school now and learns to get along with other children, he will improve.