My textbook says:
Clock arithmetic and modular systems were built upon ordinary numbers and involved familiar operations such as addition, subtraction, multiplication, and division.
So multiplication is a part of a system, but does that mean it is a system? It then states that an abstract system likely has properties such as: closure, commutative, associative, identity, inversive, and distributive. It does not define what these properties are. It also does not state what the requirements are to be classified as a system. There is no direct definition of a "system"
Then there is a question: "Is multiplication a system? Explain." What information do I need to provide to sufficiently answer this question?
I don't understand how to identify the properties of a system. What possible properties could a system have? Are a certain number of properties required in order to be classified as a system?