What is the reason behind the person having genotype I^A I^B would show the blood group as AB?

Co-dominance

In the case of co-dominance the F1 generation resembles both parents.

A good example is different types of red blood cells that determine ABO blood grouping in human beings.

ABO blood groups are controlled by the gene I. The gene (I) has three alleles I ^A , I ^B and i. The alleles I ^A and I ^B produce a slightly different form of the sugar while allele i does not produce any sugar. Because humans are diploid organisms, each person possesses any two of the three I gene alleles.

I ^A and I ^B are completely dominant over i, in other words when I ^A and i are present only I ^A expresses (because i does not produce any sugar), and when I ^B and i are present I ^B expresses.

But when I ^A and I ^B are present together they both express their own types of sugars: this is because of co-dominance. Hence red blood cells have both A and B types of sugars.