For projective space X=P​2┬áthe Landau-Ginzburg potential is f(z​1​,z​2​)=z​1​+z​2​+1/z​1​z​2. And the LG-system is given by ​z​1​-1/z​1​z​2​=z​2​-1/z​1​z​2​=0. The exceptional collection is given by {O,O(1),O(2)}. The action of the monodromies is given in the z​1 and z​2 coordinates as follows:
Action of e​2it​z​1​+z​2​+1/z​1​z​2:

​Action of z​1​+e​2itz​2​+1/z​1​z​2
​Action of z​1​+z​2​+e​2it​1/z​1​z​2
​Remark: ​ One should note that as a permutation the action is similar, in all cases, which is what is required for the definition of the quiver and the M-algined property. However, geometrically the actions are different. The fact that different monodromies can send a solution to the same end-point via different paths is crucial for the definition of the Lagrangian sections in the torpical Fukaya-Abouzaid category.