Finding a Matrix to make an equation work Here is my problem: 
Suppose $A = \begin{bmatrix}3&2\\5&4\end{bmatrix}$
and $C = \begin{bmatrix}2&0\\1&6\end{bmatrix}$
Find a matrix $B$ such that $AB=C$ or prove that no such matrix exists. Explain your answer.
In order to do this, I am going to need to find the inverse of at least one of the matrices. Will I need to find both? Help?

$AB=C$ therefore $B=A^{-1}C$ if $A$ is invertible
$det(A)=3(4)-5(2)=2$
Therefore $A^{-1}=\begin{bmatrix}2&-1\\-2.5&1.5\end{bmatrix}$
$B=$ $\begin{bmatrix}2&-1\\-2.5&1.5\end{bmatrix}$$\begin{bmatrix}2&0\\1&6\end{bmatrix}$
$$B=\begin{bmatrix}3&-6\\-3.5&9\end{bmatrix}$$
