LL(1) parsing table of left-recursive grammar
It appears you have misunderstood your professor. "If the leftmost nonterminal is S and the input is 'b', the production is both Sa and b." means that both Sa and b are correct answers if the leftmost nonterminal is S and the input is 'b'. This means that the parser does not know which production to go to and is stuck.

This means that this grammar cannot be parsed using this type of parser technology. You would either have to change the grammar or use a different type of parser.