The current that goes through A1 has to split at every instance of time between paths A2 and A3. It doesn't matter if it is AC or DC. At any instance of time Kirchhoff's rule must apply.
So if we imagine it is DC then obviously A1=A2+A3. However all that is happening with AC is that the source voltage is rising and falling, but A1 at all times must still be A2+A3.
To read current in an AC circuit we might require the ammeter to read an RMS value. This just means that the meter integrates the value of I^2 over a long period of time relative to the frequency of the source and displays the square root of this value. Maybe by measuring the heating effect in a small piece of wire.
This is the same for all the meters. This process of RMS calculation actually makes no difference because all the meters do it independently. If you imagine the source was DC then these meters would each display the square root of I^2 for each, which is just I. So if you start to increase the frequency it doesn't change anything about the calculation that A1=A2+A3.