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