Answer
The given matrice is orthogonal.
Work Step by Step
Find the inverse for matrix $A=\begin{bmatrix}
0& 1\\
-1 &0
\end{bmatrix}$:
$\begin{bmatrix}
0& 1 | 1 & 0\\
-1 &0 | 0 & 1
\end{bmatrix} \approx^1 \begin{bmatrix}
-1 &0 | 0 & 1\\
0& 1 | 1 & 0
\end{bmatrix} \approx^2 \begin{bmatrix}
1 &0 | 0 & -1\\
0& 1 | 1 & 0
\end{bmatrix}$
$1.P_{12}$
$2.M_1(-1)$
Hence, $A^{-1}=\begin{bmatrix}
0& -1\\
1 & 0
\end{bmatrix}$
Therefore, $A^T=\begin{bmatrix}
0& -1\\
1 & 0
\end{bmatrix}$
Since $A^T=A^{-1}$, the given matrice is orthogonal.
