I take A to be a matrix.
Determinant=1(7-24)-5(-21+12)-2(18-3)=-17+45-30=-2.
Reorientate:
[1 3 -3]
[5 -1 6]
[-2 4 -7]
Now we find the elements of a new matrix:
[(7-24) (-35+12) (20-2)]
[(-21+12) (-7-6) (4+6)] =
[(18-3) (6+15) (-1-15)]
[-17 -23 18]
[-9 -13 10]
[15 21 -16]
Now apply the signs matrix:
[-17 23 18]
[9 -13 -10]
[15 -21 -16]
Now divide by the determinant -2:
[8.5 -11.5 -9]
B=[-4.5 6.5 5]
[-7.5 10.5 8]
If this is correct (!) then A x B=I:
[1 5 -2][8.5 -11.5 -9]
[3 -1 4][-4.5 6.5 5] =
[-3 6 -7][-7.5 10.5 8]
[1 0 0]
[0 1 0]
[0 0 1]
Looks like we struck lucky!