Final answer:
The true statement about membrane composition is that the inner and outer membranes of mitochondria have different protein compositions, as the lipid and protein content varies with the specific functions of each membrane.
Step-by-step explanation:
The statement that is TRUE about the composition of membranes is that the inner and outer membranes of mitochondria have different protein compositions. This diversity is due to the specific functions that these membranes perform. All biological membranes contain cholesterol is not true because some prokaryotic organisms do not have cholesterol in their membranes.
It is also incorrect to say that free fatty acids are major components of all membranes, as the major membrane constituents are phospholipids and proteins. Lastly, the statement that the lipid composition of all membranes of eukaryotic cells is essentially the same is false, as the lipid and protein compositions vary based on the specific functions of each membrane.