Problem Solving

What does the circle symbol mean? and isn't this a part of number operations like a*b=b*a

it doesn't mean anything, it's just a formula that they've given, defined by that equation.

The circle symbol defines a function.

=>isn't this a part of number operations like a*b=b*a
in your example * defines multiplication. Multiplication is a function. How do you multiply? That is the rule that is pre-defined and that does not need explanation.

In the same way, the circle symbol defines a new function, and the value for this function has to be achieved using the given formula.

For more information see here:
https://en.wikipedia.org/wiki/Real-valued

I believe the answer was I,II, and III but if the is the case how does
a * 0 = a


shouldn't it be a * 0 = 0?