Answer
Since A$A^{T}$ $\ne$ I, the matrix is not orthogonal.
Work Step by Step
If a matrix is orthogonal, then A$A^{T}$ = I. If a matrix is orthogonal, then the inverse of the matrix is equal to $A^{T}$.
First, we determine if A$A^{T}$ = I.
A = $\begin{bmatrix}
1 & 1 \\
1 & -1
\end{bmatrix}$ $A^{T}$ = $\begin{bmatrix}
1 & 1 \\
1 & -1
\end{bmatrix}$
A$A^{T}$ = $\begin{bmatrix}
1 + 1 & 1 + (-1) \\
1 + (-1) & 1 + 1
\end{bmatrix}$ = $\begin{bmatrix}
2 & 0 \\
0 & 2
\end{bmatrix}$
Since A$A^{T}$ $\ne$ I, the matrix is not orthogonal.
