Find an orthonormal basis for R^{4} consisting of eigenvectors of the matrix
A=\left[\begin{array}{rrrr}1 & -1 & -1 & -1 \\-1 & 1 & -1 & -1 \\-1 & -1 & 1 & -1 \\-1 & -1 & -1 & 1\end{array}\right].
Find an orthonormal basis for R^{4} consisting of eigenvectors of the matrix
A=\left[\begin{array}{rrrr}1 & -1 & -1 & -1 \\-1 & 1 & -1 & -1 \\-1 & -1 & 1 & -1 \\-1 & -1 & -1 & 1\end{array}\right].