Find the remainder of$\displaystyle 100^{11}+1$ divided by $\displaystyle 11$

100 is equivalent to 1 (mod 11) and 1 is equivalent to -10 (mod 11).

Thus, $\displaystyle 1^{11}+-10=-9$. But -9 is equivalent to 2 (mod 11). Thus, the remainder is 2.

Correct?