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How can I create a cost distance matrix between polygons in the same layer?

Question asked by taralal on Jun 15, 2017
Latest reply on Jun 15, 2017 by xander_bakker

I'm trying to make a table of distances between each polygon in a layer but I want to do that using cost distance not Euclidean distance. I've made a cost distance raster but now I can't find a tool that will tabulate the distance between each polygon. Can this be done using polygons or would I have to use point data and even then why tool would do that? The near tool uses straight line distances. 

Any thoughts would be very helpful.