Let $A$ be a 2 by 8 , $B$ be a 8 by 6 and $C$ be a 6 by 2 matrix. Determine the size of the following matrices (if they do not exist, type N in both answer boxes):

$AB$: by
$BA$: by
$A^T B$: by
$BC$: by
$ABC$: by
$CA$: by
$B^T A$: by
$BC^T$: by