Is R=((1,2),(2,2),(1,1)) a transitive relation?

Given R ={(1,2), (2,2), (1,1)}

 

A relation is Transitive if for (x,y) and (y,z) in R implies (x,z) is in R.

This given relation is transitive as

For (1,2) and (2,2) in R implies (1,2) is in R.

Also for (1,1) and (1,2) in R implies (1,2) is in R.

 

Note for (2,2) and (2,2) in R implies (2,2) is in R.