step-by-step
\begin{pmatrix} \frac{1}{\sqrt{6}} & \frac{1}{\sqrt{6}} &-\frac{2}{\sqrt{6}} \\ \frac{1}{\sqrt{2}} &-\frac{1}{\sqrt{2}} & 0 \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}}\end{pmatrix}\begin{pmatrix} 2 &-1 & 2 \\ -1 & 2 & 2 \\ 2 & 2 &-1 \end{pmatrix}\begin{pmatrix} \frac{1}{\sqrt{6}} & \frac{1}{\sqrt{6}} &-\frac{2}{\sqrt{6}} \\ \frac{1}{\sqrt{2}} &-\frac{1}{\sqrt{2}} & 0 \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}}\end{pmatrix}^{T}
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