Step 1: Understanding the Badami Caves
- The Badami caves are a group of rock-cut temples located in Badami, Karnataka, India. They are famous for their historic significance and intricate carvings. These caves were originally carved out in the 6th century and represent the early Chalukya style of architecture.
Step 2: Analyzing the options
- (A) Aihole: Correct. The Badami caves are located near Aihole in Karnataka, which was the capital of the Chalukya dynasty.
- (B) Mirzapur: Mirzapur is not the location of the Badami caves. It is located in Uttar Pradesh.
- (C) Raigarh: Raigarh is not related to the Badami caves. It is located in Maharashtra and is not associated with these rock-cut temples.
- (D) Aurangabad: Aurangabad is known for the Ajanta and Ellora caves, not the Badami caves.
Step 3: Conclusion
Thus, the correct answer is (A) Aihole, as the Badami caves are located near Aihole, Karnataka.
\[
\boxed{\text{Correct Answer: (A) Aihole}}
\]