In an ecosystem, sun is the ultimate source of energy. The solar energy is converted into chemical energy by plants and is stored in them. This energy is then passed to other organisms as they feed on producers. The transfer of energy from one trophic level to other follows 10 percent law according to which only 10% of the energy is passed from one trophic level to next and rest of the energy is lost in respiration and in the form of heat. Thus, energy within an ecosystem is not fixed.
Hence, the statement given in the question is not correct.
So, the correct answer is 'False'.