Nitrifying bacteria, such as those in the genus Nitrobacter, are autotrophic organisms. They obtain their energy from inorganic compounds, specifically by converting ammonia or nitrite into nitrate. This process is essential in the nitrogen cycle. They are not eukaryotes, and their energy conversion does not involve mitochondria as in eukaryotic cells. Therefore, the correct answer is (A).
Final Answer:
\[
\boxed{(A) \, \text{They are autotrophs.}}
\]