Step 1: Blood group A in the child means the genotype is I$^{\text{A}}$I$^{\text{A}}$ or I$^{\text{A}}$i.
Step 2: The father has blood group B (genotype I$^{\text{B}}$I$^{\text{B}}$ or I$^{\text{B}}$i) and the mother has blood group AB (genotype I$^{\text{A}}$I$^{\text{B}}$).
Step 3: For the child to have blood group A, they must inherit I$^{\text{A}}$ from the mother (since the father cannot provide I$^{\text{A}}$) and either i or I$^{\text{B}}$ from the father. Since the child’s phenotype is A, the father must contribute i, making his genotype I$^{\text{B}}$i, and the child’s genotype I$^{\text{A}}$i.
Thus, the correct genotypes are Father: I$^{\text{B}}$i, Mother: I$^{\text{A}}$I$^{\text{B}}$, Child: I$^{\text{A}}$i.