Assuming that all matrices are and invertible, solve for :

I realized that I would someone have to reduce everything to the right of to and everything to the left would be

So for the "right side", I started with since and therefore:

would result in

For the "left size", I started with since

Multiplying the "left" with the "right" to satisfy the whole equation, I ended up with:

Is this correct, or at the very least is my though process correct and if so, what possible errors are there? Thank you.