I've got $A - B(A./C) = D$, and I want to solve for $A$.*
$A$ is an unknown 2x1 vector, $B$ is a known 2x2 matrix, $C$ is a known 2x1 vector, and $D$ is a known 2x1 vector.
*The notation $A./C$ means each element of A is being divided by an element that has the same index in $C$. So, if $A$ = \begin{bmatrix}1\\3\end{bmatrix} and $C$ = \begin{bmatrix}2\\3\end{bmatrix} then $A./C$ = \begin{bmatrix}0.5\\1\end{bmatrix}.
If $C$ is known, then a diagonal matrix $C'$ can be created with its $i$th diagonal element equals to the reciprocal of the $i$th element in vector $C$. Then $A./C = C'A$.
The matrix equation can then be factorised and then solved: $$\begin{align*} A - B(A./C) &= D\\ IA-BC'A &= D\\ (I-BC')A &= D \end{align*}$$