Step 1: Recall the genotype for blood group O.
Blood group O is homozygous recessive, written as $ii$. The child must get one $i$ from the father and one $i$ from the mother.
Step 2: State the requirement on parents.
For an O child to be possible, BOTH parents must carry at least one $i$ allele to pass on.
Step 3: Check option 1.
Father $I^A I^B$ has no $i$ allele at all, so he can only give $I^A$ or $I^B$. He can never contribute the $i$ needed for an O child. This combination is NOT possible.
Step 4: Check option 2.
Father $I^A i$ and Mother $I^B i$ both carry $i$, so an $ii$ child can appear. This is possible.
Step 5: Check options 3 and 4.
In $I^A i$ crossed with $I^A i$, and in $I^B i$ crossed with $I^B i$, each parent again carries $i$, so an O child can be produced in both. These are possible.
Step 6: Pick the impossible one.
Only option 1 fails, because the father lacks the recessive $i$ allele.
\[ \boxed{\text{Father : } I^A I^B \text{ and Mother : } I^A i} \]