Actually, there are two different issues here.

Sticking material on the walls helps only to cut down the reflected sound within a room. For example, in a theatre or cinema, panels or soft materials are fixed to the walls to absorb sound rather than reflect the sound which would create the 'echo' effect. It does not help to prevent sound from travelling from one room through the walls/ceiling to the next room.

To prevent sound from travelling from one room to the next room, you need to have solid walls (brick or concrete) full height to the floor slab without gaps or openings (air-tight). Normal gypsum board partitions are no good to block the noise as they are light and have a lot of gaps. Furthermore, the partition is usually constructed up to the suspended false ceiling level with the space above empty. Noise can also go through the suspended ceiling easily.