No full solutions to homeworks, only guidance!
The new matrix is in math called the inverse matrix of the original. You can find it by solving V1, I1 from the equations which the matrix present. In numerical cases one can use software. For ex. Excel can find the inverses of numerical matrices. Complex numbers are accepted. But your case is not numerical because A,B,C,D are variables.
The inverse does not always exist. That's the case when several inputs can cause the same output.
The inverse of a 2x2 matrix is so simple and often used that many people remember the inversion result as a general formula. It's shown also here:
https://support.office.com/en-us/article/minverse-function-11f55086-adde-4c9f-8eb9-59da2d72efc6 ADD: the general 2x2 inversion formula seems to be given already in a comment, too.
If you compare the general inversion formula and what the inversion should be in your case, you can decide what A,B,C,D values are possible. There of course are several possible circuits which fullfill the resulted equation, but the simplest possible do not need many lines to draw.