Modifying the User Groups Synchronized from On-Premise AD

Question

Hi Friends,

 

I have Synchronized Users & User Groups from my On-Premise AD to Azure AD.

 

As you all know,  User Groups synced from On-Premise AD will be having their "Source" as "Windows server AD" while User Groups Created in Azure Ad have their "SOURCE" as "Cloud".

 

I Can add / remove users to/from any USER GROUP created in AZURE CLOUD while I'm not able to add / remove users to/from USER GROUPS synced from On-Premise AD.

 

Why is it so ??

 

And, USERS or USER GROUPS created in Azure AD are not synchronized back into On-Premise AD.

 

 My question is , does the synchronization is BI-DIRECTIONAL i.e from AZURE-AD to ON-PREMISE AD and vice versa or it happens in just one direction i.e ON PREMISE AD to AZURE - AD ??