Given three vectors \(\mathbf{a}, \mathbf{b}\) and \(\mathbf{b}\) show, making use of the representation with the determinant that: \((\mathbf{a} \times \mathbf{b}) \cdot \mathbf{c}=\mathbf{a} \cdot(\mathbf{b} \times \mathbf{c})=\mathbf{b} \cdot(\mathbf{a} \times \mathbf{c})\). If not, the definition of parallelepiped volume would have been problematic.