Step 1: Understanding the Concept
In a perfectly elastic collision there is no loss of mechanical energy. Both momentum and kinetic energy are conserved.
Step 2: Detailed Explanation
So the total kinetic energy before the collision equals the total kinetic energy after it. This is (A).
(B) and (C) would describe a gain or loss of kinetic energy, which only happens in other types of collision. (D) is wrong because the coefficient of restitution is 1 for a perfectly elastic collision, not 0 (0 is a perfectly inelastic collision).
Final Answer:
Kinetic energy before equals kinetic energy after, option (A).
\[ \boxed{KE_{\text{before}} = KE_{\text{after}}} \]