Let A = {1,2,3}

(a) How many one-to-one functions are there from A to A?

(b) List all one-to-one functions onto A?

So far I have this:

(a) I believe the answer is 6, NOT SURE.

(b)

f1: A A

1 to 1

2 to 2

3 to 3

f2: A A

1 to 2

2 to 3

3 to 1

f3: A A

1 to 3

2 to 1

3 to 2

NOT SURE IF I ANM RIGHT? ANY HELP WOULD BE GREAT. THANK YOU!