Grammar to DFA conversion


construct a dfa equivalent to the grammar S->aS | bS | aA, A->bB, B->aC, C->.


Assuming that ^ is a terminal, the grammar suggests that it accepts all the strings that start with either a or b but have even lenght and null string is not accepted. So, the DFA would be:
Qstart—a, b–>Q1—a,b–>Qf—a,b–>Q1.
Where Qstart is the starting state and Qf is the final state.