Me and a friend were debating the following. For the elementary reaction
$$\ce{A + B -> A + C}$$
my friend says that it is unimolecular because $\ce{A}$ does not "participate" in the reaction. So, he says that the rate law is
$$\text{rate} = k[\ce{B}].$$
But, I think that that since it is an elementary reaction step, you cannot cancel $\ce{A}$ from both sides. I think that it is a bimolecular reaction with
$$\text{rate} = k[\ce{A}][\ce{B}].$$
Who is correct?