Mental Stretch

[J Sim]

Actually zero is a multiple of 9
9*0=0

Why it works
All numbers can be represented as 10*x + y from step one
Subtract x+y in the second step gives
[10*x+y] - [x+y] = 9*x + 0
So as long as they put the same symbol in 0 and all multiples of 9 in the table the correct symbol is always the same.

You might also notice in the table that once the numbers exceed 81 there is no need to have the 9 multiplier symbol in the 90th and 99th slot since the maximum result in step two is 81. They actually put the 9 multiplier symbol in the 86th slot.