IAIARr is the genotype of the mother.
The blood groups are the heredity characteristics of the individual which governs what antigen will be present in blood and what antibody will be present in the blood plasma.
The blood group has the genetic characteristics where A and B are dominant characters and O is the recessive character. Co Dominance is seen in case of blood grouping. Similar characteristics is seen with Rh character too where Rh positive is the dominant character and Rh negative is recessive.
The father has both the recessive characteristics. So he needs to be genetically homozygous which means that he has genetic setup of IoIo and rr.
Two child born has character of A blood group and rh positive, but the other child is A blood grouped and rh negative.
So the mother ought to be heterozygous with respect to Rh group, but she is homozygous with respect to blood group.
So her genetic setup is IAIARr.