Does this 3NF decomposition have lossless join and is it also in BCNF?

Question

I have this Relation and Functional Dependency:

R = {A, B, C, D, E, G}
FD = E->D 
     C->B 
     CBE->AG 
     B->A 
     G->E

I tried to normalize using 3NF and got:

After minimizing the FDs, I got E->D, C->B, CE->G, B->A, G->E

So resulting decompotision is: {ED, CB, CEG, BA, GE}

Assuming this is correct, CEG is a superkey

Does this mean that this decomposition has lossless join and dependency preserving?

How can I tell if this decomposition also in BCNF?