How to calculate these matrices? - explanation of the procedure Can you please help me solve this problem? I have got these matrices
$A=\left(\begin{array}{ccc}
2 & 1 & 0 \\
0 & 1 & 2 \\
3 & 0 & 1
 \end{array}\right)
$, 
$B=\left(\begin{array}{ccc}
2 & 1  \\
0 & 1  \\
3 & 0 
 \end{array}\right)
$ and
$C=\left(\begin{array}{ccc}
2 & 1 & 0  \\
0 & 1  & 2
 \end{array}\right)
$.
The task is to calculate these matrices: $(CA^{-1})$ and $(A^{-1}B)$.
In my textbook there is a hint. According to the author we should calculate $(A^T|C^T)$ to gain $X^{T}=(CA^{-1})^{T}$. Then it should be easy to convert back to $(CA^{-1})$. 
Regarding $(A^{-1}B)$ there is a hint: "Use $(A|B)$."
I tried to use these hints a while ago and both worked well. The problem is that I do not know why I used it. Can you please explain to me this procedure?
Thanks

Here $A$ is an elementary matrix so applying $A^{-1}$ from right to any other matrix would mean that you are applying the inverse operations (inverse to what was done in case of columns when applying A itself to that matrix from the right ) on the columns of that matrix.
