I don't understand why you can do one and not the other (which is not really "more complicated").

First, do you understand that matrix multiplication is NOT commutative? That is, you need to be careful about on which side you multiply.

You have

Okay, just as you did before, eliminate the "[tex]A^{-1}[/itex] on the left of the left side by multiplying both sides by Aon the left

Now eliminate the "A" on the right of the left side by multiplying both sides by on the right

Can you continue from here?