Matrix product properties for isolation of a matrix I think it should be pretty easy to have a reply to this question but I am not able to figure it out so far.
I have 2 rows:
(1) $a^TC \in \mathbb{R}^{1\times3}$ 
(2) $a^TBC \in \mathbb{R}^{1\times3}$
where 
$a \in \mathbb{R}^{3\times1},B \in \mathbb{R}^{3\times3},C \in \mathbb{R}^{3\times3}$
EDIT : $B$ is a skew-symmetric matrix (I don't know if it can help)
EDIT : $C$ is invertible
I would like to express (2) as a function of (1)
(Is there a way to isolate the term $a^TC$ or $(a^TC)^T$? )
Thanks a lot

We could write
$$
a^TBC= (a^TC)(C^{-1}BC)
$$
