Final answer:
After the Civil War, NCOs were trained at The Infantry School at Fort Benning and The Noncommissioned Officer Academy, initially known as The NCO School at Fort Sill.
Step-by-step explanation:
The question asks about the two schools that trained Non-Commissioned Officers (NCOs) after the Civil War. The two schools were The Infantry School at Fort Benning, Georgia, and The Noncommissioned Officer Academy, which began as The NCO School at Fort Sill in 1969. These institutions were established to provide advanced education and training to the NCOs, who are often referred to as the backbone of the military due to their critical role in training, leading, and caring for junior enlisted soldiers.