(a) Construct a modulo 3 addition table.

(b) Is the system closed? Explain.

(c) Is there an identity element in the set? If so, what is it?

(d) Does every element in the set have an inverse? If so, list the elements and their inverses.

(e) The associative property holds for the system. Give an example. 

(f)  Does the commutative property hold for the system? Give an example. 

(g) Is the system a commutative group? 

(h) Will every modulo system under the operation of addition be a commutative group? Explain.