For how many different pairs of numbers, a and b, are the following equalities true:

Question

a+b=a*b=a/b
???????
Thank you for your help.

Answer 1

if a*b = a/b then b^2 = 1

If b=1, then a+b = a*b is never true

If b = -1, then
a-1 = -a
a = 1/2