100 is equivalent to 1 (mod 11) and 1 is equivalent to -10 (mod 11).
Thus, . But -9 is equivalent to 2 (mod 11). Thus, the remainder is 2.
Correct?
For similar cases you could also use Fermat's Little Theorem. Since 100 and 11 are relatively prime with 11 a prime, we have , then and 100 is congruent to 1 modulo 11. So .