Final answer:
The impossible genotype for the mother, given the son's type A (IA,i) blood and the father's type AB (IAIB) blood, is type O (ii), as this would not allow for an A or B allele to be inherited by the son.
Step-by-step explanation:
The question pertains to the inheritance of ABO blood types and the possible genotypes of parents based on their offspring's blood type. With a child having blood type A (IA,i) and the father being blood type AB (IAIB), the mother cannot have blood type O (ii) as this genotype would not provide an A or B allele necessary for the father's AB genotype. Therefore, the impossible genotype for the mother is blood type O (ii).
For a son with blood type A (IA,i) and a father with type AB (IAIB), the mother's genotype must contribute an 'i' allele since the son is heterozyous (IA, i). The mother could be genotype IAIA, IAi, or IBi, but she cannot be ii, as this would result in a child with type O blood, which is not the case.