The remainder of the division of $2^{100}$ by $11$ is $1$?

The remainder of the division of $2^{100}$ by $11$ is $1$?

$$2^{10}\equiv
1\;\text{mod}\;11\Longrightarrow(2^{10})^{10}\equiv1^{10}\;\text{mod}\;11\Longrightarrow2^{100}\equiv1\;\text{mod}\;11\;\;?$$$$$$Soon,
the rest will be $1$, correct?