Value of the frequency factor in the Arrhenius equation Is the value of 'A' necessarily the same for two different reactions taking place at the same temperature?

It's actually a part of another question which is if the rate constant k1 of a reaction is found to be double that of rate constant k2 of another reaction the relationship between corresponding activation energies of the two reactions at the same temperature (e1 and e2) can be represented as e1__e2
The Arrhenius constant, A, does not have to necessarily be the same for two reactions taking place at the same temperature, due to the fact that it depends on the order of a reaction as well as the frequency with which successful collisions will occur during a reaction.

As for the second part, as k ∝ x-Ea, for 2k to be a larger value, Ea for 2k would have to be less than the one for k, i.e. e1 &lt; e2 if the activation energy for 2k is e1 and that for k is e2.