The inverse of the matrix $\left[\begin{array}{cc}2 & -1 \\ 1 & 0\end{array}\right]$ is

$\left[\begin{array}{cc}0 & 1 \\ -1 & 2\end{array}\right]$

The correct answer is Option (4) → $\left[\begin{array}{cc}0 & 1 \\ -1 & 2\end{array}\right]$

$A=\left[\begin{array}{cc}2 & -1 \\ 1 & 0\end{array}\right]$

$Adj\,A=\left[\begin{array}{cc}0 & -1 \\ 1 & -2\end{array}\right]$

$A^{-1}=\frac{1}{|A|}Adj\,A=-1\left[\begin{array}{cc}0 & -1 \\ 1 & -2\end{array}\right]=\left[\begin{array}{cc}0 & 1 \\ -1 & 2\end{array}\right]$