Final answer:
The medulla is the component of the hair that has no role in hair coloring and does not exist in some types of hair, such as fine and naturally blonde hair. It forms the hair's central core but is not present in all hair types.
Step-by-step explanation:
The component of the hair that has absolutely no role in hair coloring and does not even exist in some types of hair is the medulla. This is the correct answer to the question, which is option c) Medulla. The medulla forms the central core of the hair, which is surrounded by the cortex, a layer of compressed, keratinized cells that is covered by an outer layer of very hard, keratinized cells known as the cuticle. The medulla is not present in fine and naturally blonde hair.
The hair matrix actually contains a layer of basal cells (option d), which are responsible for the production of new hair through cell division. The basal cells in the hair bulb divide and push the new cells outward to form the hair root and shaft as the hair grows. It's crucial to note that the hair matrix is a different structure and should not be confused with the medulla, which is a part of the hair shaft.