Matrix Multiplication Problem I'm working on the following problem and I can't seem to come up with the right answer. 
$$ \text{Let}:  A^{-1} =
        \begin{bmatrix}
        1 & 2 & 1 \\
        0 & 3 & 1 \\
        4 & 1 & 2 \\
        \end{bmatrix}
$$
Find a matrix such that:
$$ ACA = 
\begin{bmatrix}
        2 & 1 & 3 \\
        -1 & 2 & 2 \\
        2 & 1 & 4 \\
        \end{bmatrix}
$$
Could someone point me in the right direction? Thanks!

You have
$$
C=A^{-1}(ACA)A^{-1}.
$$
So
$$
C=  \begin{bmatrix}
        1 & 2 & 1 \\
        0 & 3 & 1 \\
        4 & 1 & 2 \\
        \end{bmatrix}\,\cdot\,
\begin{bmatrix}
        2 & 1 & 3 \\
        -1 & 2 & 2 \\
        2 & 1 & 4 \\
        \end{bmatrix}\,\cdot\,
\begin{bmatrix}
        1 & 2 & 1 \\
        0 & 3 & 1 \\
        4 & 1 & 2 \\
        \end{bmatrix}.
$$
Now you can just perform the computation. 
