[lo0dot0]

You can only get an 8 in the rightmost digit of the result by multiples of the rightmost digits, but 08 obviously gets you a 0, so fairly easy to see this is wrong.

(10a+b)(10c+d) = 100ac+10(ad+bc)+bd

[xanderlewis]

Well… I was joking. Even more generally, multiplication by b in base b gives a zero at the end.

[xanderlewis]

… and, in fact, ‘b in base b’ always looks like 10 anyway!