Matlab, 27 bytes

Using an anonymous function:

@(A)mat2str(inv(A)*det(A)')

Input is in standard Matlab format, that is, [-3,2,-5; -1,0,-2; 3,-4,1], where commas can be replaced by spaces, and spaces after ; can be removed.

Example:

>> @(A)mat2str(inv(A)*det(A)')
ans = 
    @(A)mat2str(inv(A)*det(A)')

>> ans([-3,2,-5; -1,0,-2; 3,-4,1])
ans =
[-8 18 -4;-5 12 -1;4 -6 2]

Or try it online in Octave.