Find all numbers a and b such that the matrix A is orthogonal

Question

Find all numbers $a$ and $b$ such that the matrix $$\begin{equation} A = \begin{bmatrix} a+b & b-a \\ a-b & b+a\end{bmatrix},\end{equation}$$ is orthogonal.

I've gotten to $$\begin{bmatrix} a+b & b-a \\ a-b & b+a\end{bmatrix} * \begin{bmatrix} a+b & a-b \\ b-a & b+a\end{bmatrix} = \begin{bmatrix} 2a^2 + 2b^2 & 0 \\ 0 & 2a^2 + 2b^2 \end{bmatrix}$$ Therefore \begin{equation} a = -b \end{equation} Unsure where to go from here.

Answer 1

$A$ is orthogonal $ \iff \begin{bmatrix} 2a^2 + 2b^2 & 0 \\ 0 & 2a^2 + 2b^2 \end{bmatrix}=\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix} \iff a^2+b^2=\frac{1}{2}$.