Checksum for equivalent cells in a table?

I have a sheet formatted like the following, where the rows and columns have the same entries.

In this, the value of the A-B cell should always be equal to the value of the B-A cell, and so forth. (Cells with the same row and column entry, ie A-A, will always be 0).

I'm looking for something that will verify that these values are equal, and flag when they aren't. More importantly, I want something that I don't have to do manually for a giant table that will probably have new rows added over time (which is why I'm not just making a set of =IF statements for every cell).

Thanks