Presumably, you meant to write:
rate = k*[a]*[b] ---- square brackets are used, by convention, to indicate the concentration of a species.
The
The rate gives the rate of change in concentration of the product per unit time, so is going to have units of concentration per unit time, e.g., mol/(L*s) or mol/(kg solvent * s). [a] and [b] both have units of concentration, i.e., M = molarity = mol/liter, or m = molality = mol/(kg solvent). The answer choices you gave used a lower-case "m" so I'll assume that meant molality
Putting this together yields:
m/s = k*m²
k = m/s * 1/m² = 1/(m*s) = m^-1 * s^-1
