Let’s examine each statement in the light of

$$k = A\,e^{-\frac{E_a}{RT}}\,. $$

A. “Arrhenius holds true only for an elementary homogeneous reaction.”

• False – it’s an empirical law and is routinely used (and found valid) for complex, composite or even heterogeneous processes.

B. “The unit of $A$ is the same as that of $k$.”

• True – since $e^{-E_a/RT}$ is dimensionless, $A$ must carry whatever units $k$ has.

C. “At a given temperature, a low activation energy means a fast reaction.”

• True – smaller $E_a$ makes $\exp(-E_a/RT)$ larger, hence a larger $k$.

D. “$A$ and $E_a$ as used in Arrhenius depend on temperature.”

• False – in the simple Arrhenius model both are treated as constants (over modest $T$-ranges).

E. “When $E_a \gg RT$, $A$ and $E_a$ become interdependent.”

• False – although in some data sets you observe a correlation (compensation effect), the basic Arrhenius form still treats them as independent parameters.

Therefore the only correct statements are B and C.

Answer: B and C only.