 In practical terms, a comparable statement is that any orthogonal matrix can be produced by taking a rotation matrix and possibly negating one of its columns, as we saw with matrices.If is odd, then the semidirect product is in fact a direct product, and any orthogonal matrix can be produced by taking a rotation matrix and possibly negating all of its columns.This follows from the property of determinants that negating a column negates the determinant, and thus negating an odd (but not even) number of columns negates the determinant.