 The matrices have the form

which orthogonality demands satisfy the three equations

In consideration of the first equation, without loss of generality let , ; then either , or , .We can interpret the first case as a rotation by (where is the identity), and the second as a reflection across a line at an angle of .The special case of the reflection matrix with generates a reflection about the line at 45° given by and therefore exchanges and ; it is a permutation matrix, with a single 1 in each column and row (and otherwise 0)