(*  stepwise calculation of an inverse matrix, using matrix operations  *)

matA = {{5, 4}, {2, 1}};

Print("by Identity\n", matA . IdentityMatrix(2));
Print("by Inverse\n", matA . Inverse(matA));


(*  adjoint(matA)  *)
Aadj = Transpose(matA . {{0, -1}, {1, 0}}) . {{0, -1}, {1, 0}};
Print("Adjutant\n", Aadj);
Print("Inverse\n", Inverse(matA));

(*  Flatten(Minors(matA, 2)) = {Det(matA)}  *)
Print("calculated Inverse\n", (IdentityMatrix(2) / Det(matA)) . Aadj);