Step 1: Start from the one fact that decides both statements.
The position of a chemical equilibrium is fixed entirely by the equilibrium constant $K$, and $K$ depends only on temperature. Anything that leaves both the partial pressures (or concentrations) of the reacting species and the temperature unchanged cannot shift the equilibrium, whatever else it changes.
Step 2: Apply this to Statement A.
Adding an inert gas at constant volume raises the total pressure, but it does not squeeze the reacting molecules into a smaller space or change how many moles of each reactant and product are present. Their partial pressures stay exactly as before, so the equilibrium does not move. Statement A is correct.
Step 3: Apply the same fact to Statement B.
A catalyst changes the mechanism by lowering the activation energy for both the forward and reverse reactions equally. It gets the system to equilibrium faster, but it does not touch $\Delta G$, so it cannot change $K$ or the equilibrium concentrations themselves. Statement B is correct for the same underlying reason as Statement A.
Step 4: Notice both statements are really the same principle in two disguises.
One is a physical change (adding gas) that leaves partial pressures alone, the other is a kinetic tool (a catalyst) that leaves the thermodynamics alone. Both fail to alter $K$, so both fail to alter the equilibrium position.
Final Answer:
\[ \boxed{\text{Both statements are correct}} \]