First we have to figure out whether the allele controlling for that trait is dominant or recessive. From female A, the pedigree indicates that she shows the trait, but neither of her parents shows the phenotype of the trait. Female A is only possible to have the trait showed if both of her parents carry an allele of the trait. So, that allele for controlling the trait should be recessive and their parents are heterozygous as neither of the parents shows it in their phenotype.
After we figured out the allele is recessive, we can easily determine the genotype of female A. Traits that are controlled by recessive alleles can only be shown in phenotypes if theres no dominant allele existing. Therefore, the genotype of female A must be both recessive, and that means she's homozygous (recessive).
