Step 1: Recall the definition of absolute ceiling.
The absolute ceiling is the maximum altitude at which an aircraft can maintain level flight.
At this altitude,
\[
\boxed{
\text{Excess Power}=0.
}
\]
Step 2: Relate excess power to rate of climb.
Since
\[
\text{Rate of Climb}
=
\frac{\text{Excess Power}}{\text{Weight}},
\]
when the excess power becomes zero,
\[
\boxed{
\text{Maximum Rate of Climb}=0.
}
\]
Therefore,
\[
\boxed{\text{Maximum rate of climb is }0}
\]
is the correct answer.
Thus,
\[
\boxed{(A)}
\]
is the correct answer.