# How to find the units of the rate constant?

Consider the reaction $$\ce{2A + B -> Products}$$ When the concentration of $\ce{B}$ alone was doubled, the half-life did not change. When the concentration of $\ce{A}$ alone was doubled, the rate increased by two times. The units of the rate constant is:

a) $\mathrm{s^{-1}}$

b) $\mathrm{L\ mol^{-1}\ s^{-1}}$

c) Unitless

d) $\mathrm{mol\ L^{-1}\ s^{-1}}$

I have tried it solving through this method:

According to me, when the concentation of A alone was doubled, reaction rate also increased by two time, implies that Reaction is first order according to A. In same way, the reaction should be 0 order according to B. So net order would be 1. So this gives me answer $\mathrm{s^{-1}}$ but the answer is $\mathrm{L\ mol^{-1}\ s^{-1}}$. Where am I going wrong?

$t_{1/2} = \ln2 / K$