Answer
$\begin{bmatrix}
1&-1\\
-1&2
\end{bmatrix}$
Work Step by Step
Using the formula,
$A^{-1} = \frac{1}{|A|}\times{Adj(A)}$
$where, A = \begin{bmatrix} 2&1\\1&1\end{bmatrix}$
$Adj(A) = \begin{bmatrix}d&-b\\-c&a\end{bmatrix}, if A = \begin{bmatrix}a&b\\c&d\end{bmatrix}$
$\implies A^{-1} = \frac{1}{(1)(2)-(1)(1)}\times \begin{bmatrix}1&-1\\-1&2\end{bmatrix}$
$=1\times \begin{bmatrix}1&-1\\-1&2\end{bmatrix} = \begin{bmatrix}1&-1\\-1&2\end{bmatrix}$
