Groups and the Group Axioms · Challenge problem

Let $A=\begin{pmatrix}2&1\\1&1\end{pmatrix}$, $B=\begin{pmatrix}1&1\\0&1\end{pmatrix}$, $C=\begin{pmatrix}1&0\\1&1\end{pmatrix}$, with respective inverses $\begin{pmatrix}1&-1\\-1&2\end{pmatrix}$, $\begin{pmatrix}1&-1\\0&1\end{pmatrix}$, $\begin{pmatrix}1&0\\-1&1\end{pmatrix}$. If $X=(ABC)^{-1}$, find the $(1,1)$ entry of $X$.