Service tax on works contract

Dear All! I need some clarification on the following area. A ltd co receives an erection service from B, an individual who is exempted under service tax, being an SEZ unit,. Therefore, B has not charged service tax in his invoice. Is A ltd liable to pay 50% of the invoice amount as service tax under reverse charge mechanism to the govt? If so paid, are they eligible to avail credit of the amount so paid? Thanks in advance! Please clarify