AdjointMatrix[M_] := Module[{Ma, B, n, i, j}, Ma = Minors[M];
   B = Ma;
   n = Dimensions[M][[1]];
   For[i = 1, i <= n, i++,
    For[j = 1, j <= n, j++,
     B[[i, j]] =
       Ma[[n + 1 - i,
          n + 1 - j]]*(-1)^(i + j);];(*inner for*)];(*outer for*)
   Transpose[B]];