Centre of Mass and Collision Part 1

Kinetic energy of a system of particle is zero this is possible only when the speed of each particles is zero. And if speed of each particle is zero, the linear momentum of the system of particle has to be zero.
Also the linear momentum of the system may be zero even when the particles are moving in different direction. This is because linear momentum is a vector quantity. In this case the kinetic energy of the system of particles will not be zero.
∴A does not implies B but B implies A.