If i understood well, you need to find the matrix X witch suffices
Sure you can't really divide one matrix by another, as this is not defined.
Notice that my matrix X is your matrix A. You can find X by solving the system. To do so, you create the associated matrix of the system and put it into reduced by rows form.
If you're not supposed to know how to resolve linear systems escalonating matrices, you can assume , do the multiplication and then equal the matrices, term by term. Please notice that this is what you'll be doing with the row reduction process.
I'm not going into the details of row-reducing right here, you should check your textbook for the algorithm. Mathematica yields me the row reduced associated matrix as being
And so, the matrix X (or A, in your post) that you are looking for is:
If you have a doubt in some part of the solution, feel free to post back,