Demonstration: Elastic Collision Between Equal Masses

A ball A of mass m and speed v0 undergoes a head-on elastic collision with a ball B of the same mass m, initially at rest. Show, starting from the conservation of momentum and the conservation of kinetic energy, that ball A stops after the collision (v1' = 0) and that ball B moves off with speed v0 (v2' = v0). Detail every step of the calculation.