Solution VO.T07 Chris Black

\begin{align*} \zerovector &= c\zerovector + (-c\zerovector)&&\knowl{./knowls/property.AIC.knowl}{\text{Property AIC}}\\ &= c(\zerovector + \zerovector) + (-c\zerovector)&&\knowl{./knowls/property.ZC.knowl}{\text{Property ZC}}\\ &= (c\zerovector + c\zerovector) + (-c\zerovector)&&\knowl{./knowls/property.DVAC.knowl}{\text{Property DVAC}}\\ &= c\zerovector + (c\zerovector + (-c\zerovector))&&\knowl{./knowls/property.AAC.knowl}{\text{Property AAC}}\\ &= c\zerovector + \zerovector&&\knowl{./knowls/property.AIC.knowl}{\text{Property AIC}}\\ &= c\zerovector&&\knowl{./knowls/property.ZC.knowl}{\text{Property ZC}} \end{align*}