For a positive integer $n$, let $A(n)$ be the equal to the remainder when $n$ is divided by $11$ and let $T(n)=A(1)+A(2)+A(3)+ \dots + A(n)$. Find the value of $$A(T(2021))$$
Source: Bangladesh Mathematical Olympiad 2021 Problem 1
Tags: algebra, functional equation
For a positive integer $n$, let $A(n)$ be the equal to the remainder when $n$ is divided by $11$ and let $T(n)=A(1)+A(2)+A(3)+ \dots + A(n)$. Find the value of $$A(T(2021))$$