I am told this matrix is supposed to be orthogonal, but when I multiply it by itself (its transpose), I get 7/4 on the diagonal and not 1. Does an orthogonal matrix have to be 1's on the diagonal?
\begin{pmatrix}\frac{1}{2}&-\sqrt{\frac{3}{2}}\\ -\sqrt{\frac{3}{2}}&-\frac{1}{2}\end{pmatrix}