Can vectors be inverted? I wish to enquire if it is possible to solve the below for $C$.
$$B^{-1}(x-\mu) = xc $$
Here obviously $B$ is an invertible matrix and both $c$ and $\mu$ are column vectors.
Would the solution be $$x^{-1}B^{-1}(x-\mu) = c $$ is it possible to invert vectors ?
How about if it was the other way
$$B^{-1}(x-\mu) = cx $$
Is there any other way to do this ?
Thanks in advance. 

Perhaps this definition of the inverse vector will help you:
An inverse rectilinear vector   ā'  is a vector which is co-directed (in the same direction as) a vector ā and differs from it in magnitude according to: 
$$ |\bar{a'}|=\dfrac{1}{|\bar{a}|} $$
Projections on the coordinate axes of inverse rectilinear vectors are equal according to:
$$\quad a'_{x}=\dfrac{a_{x}}{a_{x}^{2}+a_{y}^{2}+a_{z}^{2}};\quad a'_{y}=\dfrac{a_{y}}{a_{x}^{2}+a_{y}^{2}+a_{z}^{2}}\quad a'_{z}=\dfrac{a_{z}}{a_{x}^{2}+a_{y}^{2}+a_{z}^{2}} $$
An example of solving problems with this vector can be found here https://en.wikipedia.org/wiki/Talk:Cross_product#Cross_product_does_not_exist
https://doi.org/10.5539/jmr.v9n5p71
