Find an orthogonal basis for $\mathbb R^3$ consisting of the eigenvectors of the matrix $$\begin{bmatrix} 1 & 2 & 2 \\ 2 & 1 & 2 \\ 2 & 2 & 1 \end{bmatrix}$$
Isn't this question basically just asking 'find the eigenvectors of this matrix'? And the part about finding 'an orthogonal basis' is irrelevant?