Mach is the ratio of an aircraft's True Airspeed (TAS) to the local speed of sound.
The local speed of sound is only dependent on temperature. Nothing else.
Therefore, it is conceivable that at a constant Mach one could cross a front and have a change to the TAS in order to maintain constanct Mach, which would require a change in IAS.
The colder the air mass, the higher the Mach number for a constant TAS
The warmer the air mass, the lower the Mach number for a constant TAS
I hope this helps... it's been a while!