Finding matrices from an inversive matrix

Hello all,

I'm trying to work on this problem for my homework, but I just can't seem to understand what to do.

I know how to calculate the inversive of a matrix but I just don't know how to approach this kind of a problem.

I was searching everywhere for some guidance on how to approach it, but I just don't understand how.

Please, I am not looking for the answer, I am just looking for the method on how to solve it.

I uploaded a picture with the question.

Thank you so much

 

Well, I read about it and found a few youtube videos that helped me understand it much better, but still I don't know what to do.

I calculated the inverse of matrix A, but then I got stuck on what should I do.

Should I get the inverse of A just divide the matrix into block matrix and try to find a matrix that replaces the values?

Thanks