(E)

Given the data in this problem, the rate law is first order with respect to both A and B, or second order overall. (This is true because each causes the reaction rate to double when the concentration is doubled.) To find the units of the specific rate constant (which are different for rate laws of different order), plug the known units into the rate equation.

          Reaction rate = k [A] [B]
          Mol/L s = k [mol/L] [mol/L]
          k = L/mol s