No! In about 21% of identical (monozygotic or MZ) twin pairs, one twin is right-handed, and the other is either left-handed or ambidextrous. Since identical twins share identical genes, this is evidence that handedness is not a totally genetic trait.
Left-handedness is more likely to occur in twins than in single individuals. Only about 10% of people in the general population are left-handed. But about 17% of all twins are left-handed.
The cause of hand preference is not well understood. It is likely to be a combination of genetic and environmental factors. Environmental factors such as stress during birth, hormone levels during pregnancy, or position in the womb have been suggested. It has also been proposed that mirror-imaging in the formation of MZ twins could cause their differences in hand preference. Cultural influences also have an effect, as parents may encourage right-handedness.
In 2019, a genome-wide analysis study examined hand preference in over 300,000 individuals using data from the UK Biobank cohort. They found that the genetic associations identified in in smaller studies were no longer significant in a very large cohort.