How to get the DPI of an image file (PNG)

You could use identify from imagemagick:

identify -format '%x,%y\n' image.png

Note however that identify will return the resolution in PPCM¹ (pixels per centimeter) instead of PPI (pixels per inch) so you might need to add -units PixelsPerInch to your command.

There's also exiftool:

exiftool -p '$XResolution,$YResolution' image.png

though it assumes the image file has those tags defined.

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^{1: see this thread on their forum}

open it with "the gimp" and click [image] -> [image properties]