Solution:

Since the gases are mixed at constant volume \( V \) and temperature \( T \), we can apply the ideal gas law for each gas:

For each gas, we have:
\[
P = \frac{nRT}{V}
\]

Since both gases have the same pressure \( P \), volume \( V \), and temperature \( T \), they contribute equally to the total pressure when mixed.

After mixing, the total pressure of the mixture is the sum of the partial pressures of each gas:
\[
P_{\text{total}} = P + P = 2P
\]

Thus, the pressure of the mixture is 2P.