Make a list of all invertible elements of z/20z along with their inverses (under the multiplication operation).

Step-by-step explanation:

We are given that

We have to find the invertible elements of along with their inverses under multiplication.

We know that

U(20)={1,3,7,9,11,13,17,19}

Operation used

Identity element=1

Inverse condition  :

Inverse of 1=1

Inverse of 3

()

Inverse of 3=7

Inverse of 7=3

Inverse of 9

Inverse of 9 is 9 .

Inverse of 11

11 is also self inverse element.

Where 1 is remainder

Hence inverse of 13 is 17 and inverse of 17 is 13.

19 is also self inverse element.

Therefore,

mr. graef told us it is 13 pints

step-by-step explanation: