Let:

A = $\displaystyle \begin{bmatrix} 1 & 1 & 0 \\ 1 & 1 & 0 \\ 0 & 0 & 2\end{bmatrix}$

B = $\displaystyle \begin{bmatrix} s+1 & 1 & 0 \\ 1 & s+1 & 0 \\ 0 & 0 & -2\end{bmatrix}$

Find an orthogonal matrix that simultaneously diagonalizes both A and B. (I've already checked to make sure they commute, now from here?