Preimage of 1 orthogonal to 1 for skew-symmetric matrix
Solution 1:
$A\mathbf{q} = \mathbf{1} \Rightarrow A\mathbf{q} \cdot \mathbf{q}= \mathbf{1} \cdot \mathbf{q}$, but the LHS vanishes by antisymmetry.
Preimage of 1 orthogonal to 1 for skew-symmetric matrix
Solution 1:
$A\mathbf{q} = \mathbf{1} \Rightarrow A\mathbf{q} \cdot \mathbf{q}= \mathbf{1} \cdot \mathbf{q}$, but the LHS vanishes by antisymmetry.