(a) Construct a modulo 7 multiplication table.

(b) Is the system closed under the operation of multiplication?

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

(d) Does every element in the set have an inverse? Make a list showing the elements that have a multiplicative inverse and list the 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 this mathematical system a commutative group? Explain.