Groups and the Group Axioms · Easy problem

Let $b=\begin{pmatrix}1&0\\1&1\end{pmatrix}$ and suppose $(ab)^{-1}=\begin{pmatrix}2&-1\\-1&1\end{pmatrix}$ for some matrix $a$. Using $(ab)^{-1}=b^{-1}a^{-1}$, find $a^{-1}$ and report the sum of its four entries.