No.
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Twins are not necessarily identical. They can be fraternal as well. Identical twins result when one fertilized egg splits in two. Fraternal twins result from two fertilized eggs.
Identical twins are the result of a single fertilized embryo splitting in two at an early stage and forming two viable embryos. As such, identical twins have identical DNA. Fraternal twins are the result of two distinct fertilized embryos being viable. As such, they have different DNA. They could even be different sexes.
If two (or more) eggs are fertilised and develop together you will get fraternal twins. Identical twins are the result of a single fertilised egg dividing into two embryos.
If they were not then they would not be called identical twins!
Identical twins are formed from a single egg that splits into two. Fraternal twins are formed from two separate eggs that are both separately fertilized. So identical twins have identical DNA, and fraternal twins do not.