Entries in the last row between columns 2 and 9 are mirror images of each other. In the last row, the sum of entries equidistant from columns 2 and 9 always sum up to 99. Looks like another case for the distributive law . One row up, the sum is 88, then 77, and so on. This diagonal entry is the average of the other two.
Some facts come up on observing addition and multiplication tables simultaneously.
Say, both are 10x10. In the lower right corner of the tables, the entries 18 and 81 are mirror images of each other. So far it was pure arithmetic. To see the pattern we have to handle several tables simultaneously. In the addition tables, it is always a two digit number with 1 followed by the penultimate digit of the system.