The sum or product of two digits may only produce one or two digit numbers. This is true in all base systems. Numbers equal in one base are equal in any other base. Conversion between bases does not violate arithmetic identities. For addition, in the lower right corner, there always appears a 2-digit number whose first digit is 1 while the second digit is the penultimate digit of the system.
All tables are symmetric with respect to the diagonal from the upper left to the lower right corner.
In the last row of multiplication tables, last digits grow by 1 if followed right to left. At the same time, the first digits decrease by 1. One can use addition tables to play the same game as with the Calendar tables . For multiplication tables this is also true provided selected entries are multiplied instead of being added up. As a particular case, in multiplication tables determinants of any 2x2 square are 0.