Given the matrix equation

$\displaystyle X^{-1}A^{T} + B^{-1}C = 0$

Where $\displaystyle A,B,C,$ and $\displaystyle X$ are 2 x 2 invertible matrices. Solve for $\displaystyle X$ in terms of $\displaystyle A,B,C$.

ii) Find X when $\displaystyle A = \begin{matrix} [1 & 1] \\ [0 & 2] \end{matrix}, B= \begin{matrix} [1 & 2] \\ [1 & 1] \end{matrix}, C= \begin{matrix} [1 & 2] \\ [1 & 4] \end{matrix}$