Binary relations and congruence

Prove that congruence n is an equivalence relation on the set (double barrel Z).

So I can show that it is symmetric because

a - b = nk

b - a = nk

(-1)(b - a) = (-1)nk

a - b = (-k)n

example

a = 1 b =2

1 - 2 = nk

(-1)(-1 = nk)

1 = (-k)n

2 - 1 = nk

1 = nk

it also seems to be reflexive because

if a = b

a - a = nk

if k was 0 that would be true

and if its reflexive and symmetric it would also be transitive

I am not sure if this work is accurate or if that final about it being reflexive and symmetric implies its transitive is correct. Any help would be greatly appreciated.