Consider the following two statements:
(A) Linear momentum of the system remains constant.
(B) Centre of mass of the system remains at rest.
We know that,
So, Centre of mass at rest means v(cm)=0, hence, linear momentum of the system must be zero.
So, B implies A. Now, Linear momentum constant means, it may be other than zero, and in that
case velocity of centre of mass will be non-zero too. Hence, A doesn’t imply B.