We are given that a and b are non-zero integers and ab >b
=> ab - b > 0 => b (a-1) > 0. There will be two cases

Case 1: Either both b and a-1 are positive
=> b > 0 and a-1 > 0
=> b > 0 and a > 1

I. a/b > 0
TRUE as both a and b are positive so a/b > 0

II. (a - b) > 0
a-b > 0, Not necessary as b can be 3 and a can be 2

III. (a + b) > 1
a + b > 1 is TRUE
as a> 1 and b> 0

Case 2: Both b and a-1 are negative
=>b < 0 and a-1 < 0
=> b < 0 and a < 1
Since, a is a non-zero integer
=> a < 0 and b < 0

I. a/b > 0
TRUE as both a and b are negative so a/b > 0

II. (a - b) > 0
a-b > 0, Not necessary as a can be -3 and b can be -2
making a-b = (-3) - (-2) = -1 which is < 0

III. (a + b) > 1
a + b > 1 is FALSE
As both a and b are negative

Combining both the cases the only option which is true in both of them is Option I

So, Answer will be A
Hope it helps!

Watch the following video to learn the Basics of Inequalities