You can easily invert the transparent parts of an image with Gimp. Gimp is an open source Photoshop alternative.
Follow these steps:
Colors -> Components -> Decomposefrom the menu and set
- A new image is opened with all color channels (including alpha channel) decomposed as single layers.
- Select the layer
Colors -> Invertfrom the menu.
Colors -> Components -> Composefrom the menu, set
RGBAand make sure the layers are correctly mapped to the channels (should default correctly if you did not reorder the layers)
It will open a few new Gimp tabs but it will, indeed, invert the transparent areas of the image. This worked well for me on an image of a single color with transparency.