replacing a 2 prong plug?

For 120 volt convenience plugs in North America it does make a difference which wire goes to which pin. The large pin is for the neutral connection, the smaller pin is the hot connection. If the wires are reversed AND the case of the device has one wire connected to it then it is possible for the case to have line voltage on the case. If this is a double insulated device it is NOT applicable.

It DOES matter.

Look more closely at the two wires. One of them will either have some printing on it, or have a ridge or ridges molded into it. (I find it easier to feel the ridges, instead of seeing them.)

The lead with the printing or ridges is the "neutral", and should go to the wider prong on your replacement plug. (Or, the silver connector, if they are silver and brass.)

Since they are the same size, it doesn't matter. The people who posted otherwise didn't read the part about the prongs being the same size. Reading is HARD!

Easy to figure out with a multi meter. Measure with multi meter voltage from each wire to ground. The wire that gives you nominal voltage between the wire and ground is your hot conductor.

jim w is correct so color wise the white wire goes to the largest prong and the black wire goes to the smaller prong in other words facing away from you (as if to plug it in) the white (neutral or negitive) is on the left while the black (hot or positive) is on the right your welcome (in advance)

No.