Give an example of a non-commutative ring of order $4?$
I found an example as follows: Let $R=\{0,a,b,c\}$ with a binary operation + defined on it.
The multiplication table is given by:
Does this suffice as an example? Or do we need to define what the operation $+$ looks like explicitly? Precisely, do I need to write out an addition table just like the multiplication table above?