Question

A wave transports energy and not matter. Justify this statement.

Answer 1

A wave transports its energy without transporting matter. Waves are seen to move through an ocean or lake; yet the water always returns to its rest position. Energy is transported through the medium, yet the water molecules are not transported. ... The same thing can be said about a stadium wave.
in simply other words ...
WAVES AS CARRIES OF ENERGY
Waves are the means of energy transfer without transfer of matter. Let us prove it with the help of an experiment.
EXPERIMENT
Drop a stone into a pond of water. Water waves will be produced on the surface of water and will travel outwards. Place a cork at some distance from the falling stone. When the waves reach the cork, it will move up and down along the motion of the water particles by getting energy from the wave.
This experiment shows that water waves like other waves transfer energy from one place to the other without transferring matter.