Let T be the centroid of a triangle $\mathrm{\u25b3}ABC$

How can I prove that (using vectors):

$\overrightarrow{TA}\times \overrightarrow{AB}=\overrightarrow{TB}\times \overrightarrow{BC}=\overrightarrow{TC}\times \overrightarrow{CA}$

($\times $ is for vector-product).

How can I prove that (using vectors):

$\overrightarrow{TA}\times \overrightarrow{AB}=\overrightarrow{TB}\times \overrightarrow{BC}=\overrightarrow{TC}\times \overrightarrow{CA}$

($\times $ is for vector-product).