a) Show that

is a commutative ring

b) Show that if

then

and

Answers

a) Is it sufficient to show that

satisfies additive commutative, associativity, identity and inverse and satisfies multiplicative associativity, commutativity and identity?

In that case

Noting that

is a commutative ring

Additive commutativity

The above statements are equal to each other, then

satisfies this property.

Multiplicative commutativty

Above 2 expressions are equal to each other, then

satisfies this property.

Do I continue in this vein with the other properties to prove that

is a commutative ring?

Part B

Is it sufficient to show that

This

and

Hence

and

Will this suffice?

Thanks for the responses in advance