You are given a matrix equation

    B - X*A = I.

where B, A and I are given  2x2-matrices.


Re-write it in the form

    X*A = C,       (1)

where  C = B - I.



Now, the matrix A is non-degenerated (since its determinant is not zero).


Therefore, the inverse matrix    does exist.

Calculate the inverse matrix  ,  using your knowledge of linear/(matrix) algebra.


Then multiply equation (1)  by the matrix    from the right side.


You will get then the solution 

    X = .