Basically, we want to try to conver the matrix into
1 0
0 1 (called I)
and record what we do on another I matrix. If an inverse exists we will be able to reduce our matrix to the I matrix. Thus we could begin:
a, b
c, d
and reduce it into row echelon form (hopefully ending in I), while keeping track of our steps with a copy of I.
Thankfully there are shortcuts that have been found, and for a 2D matrix it makes things pretty simple. Let us assume we have a matrix :
we first calculate the determinant =ad bc
Then the inverse matrix (assuming the determinant (denoted A ) is
ie:

d/(adbc), b/(bcad)

c/(bcad), a/(adbc) //notice I have eliminted the signs by swapping the order of the eq'n in the denominator

Incidentally (and I'm sure you're not really interested, but this idea can be extended for larger matrices also).
THUS: All you need to do is write code to take 4 inputs (from text boxes arranged as a matrix) and to output four labels (again arranged as a matrix) solved using the equations above. Hope this helps!!! (If you are still having trouble, I may be able to help, but as I mentioned VB is not really my forte'....)