I am computing singular value decomposition at the moment and the book gave us the left singular matrix to be $U = \begin{pmatrix} \frac{-1}{3} & \frac{2}{3}&\frac{2}{3} \\ \frac{2}{3} & \frac{-1}{3} &\frac{2}{3} \\ \frac{2}{3}& \frac{2}{3} & \frac{-1}{3} \end{pmatrix}$ for the matrix $A = \begin{pmatrix} -3 &1 \\ 6&-2 \\ 6&-2 \end{pmatrix}$
Noticed that the second column and the third column of $U$ are not orthogonal, yet the matrix still works!