some properties (axioms) multiplication

Question 1

Closure

Answer 1

Multiply two even numbers, the answer is still an even number

multiply two numbers the answer is still odd, therefore the set of odd numbers is closed under multiplication

Question 2

Commutative

Answer 2

order does not make a difference

2x3 = 3x2
does not hold for division

Question 3

Associative

Answer 3

grouping does not make a difference

(2x3) x 4 = 2x(3x4)
(axb) xc = ax(bxc)

does not hold for division

Question 4

Identity Element

Answer 4

for multiplication is 1, any number multiplied by 1 gives the original number

Question 5

multiplicative Inverse

Answer 5

the reciprocal of the number multiplied by its reciprocal equals 1

2 x 1/2 = 1, therefore, 2 and 1/2 are multiplication inverse
a x 1/a

number 0 has no multiplicative inverses