Maneuver and its Inverse (question)

[Cielo]

S = B D2 R U B D' R D2 F U D' B2 D' L2 D' F2 R2 B2 D2 R2
M1 = B2
S M1 has two blocks: DB&DBL (now in RU&RUB), LB&LBU (now in UL&ULB).
For the first one, X = z y', so after executing S M1 X, DB&DBL are "solved". As a result, DB&DBL are also "solved" if we execute X' M1' S'.
In fact, DB&DBL block is in RU&RUB after X'. So M1' S' moves the RU&RUB block to DB&DBL.

After writing down this, I find my explanation was too complicated -_-| But It still can answer your question in the first post.
Just as qqwref posted: S moves a block from position A to B, then S' moves a block from position B to A.

[siva.shanmukh]

S = B D2 R U B D' R D2 F U D' B2 D' L2 D' F2 R2 B2 D2 R2
M1 = B2
S M1 has two blocks: DB&DBL (now in RU&RUB), LB&LBU (now in UL&ULB).
For the first one, X = z y', so after executing S M1 X, DB&DBL are "solved". As a result, DB&DBL are also "solved" if we execute X' M1' S'.
In fact, DB&DBL block is in RU&RUB after X'. So M1' S' moves the RU&RUB block to DB&DBL.

After writing down this, I find my explanation was too complicated -_-| But It still can answer your question in the first post.
Just as qqwref posted: S moves a block from position A to B, then S' moves a block from position B to A.

Okay.. I got what you are trying to say. But the best answer would be your last line and qqwref's answer

[mariano.aquino]

This I already knew. I mean if there is a set of solved cubies, they would be solved in the inverse maneuver as well. My question is regarding unsolved blocks. Anyways don't bother, I got my answer from qqwref's reply



In FMC, if you are stuck at a point, say right after solving a 2x2x2 block (by saying stuck, I mean not getting any optimal maneuver from there on), you could just invert the scramble and the partial solution you have got so far on a solved cube and try to proceed from there. This not only gives a different unsolved state with the same solved block, but also lets you use it as your solution. for example if Ma S Mb renders the cube solved where S is your scramble, then Mb Ma is a solution for S. You can prove it in the following way.

Ma S Mb = I
Ma' Ma S Mb Ma = Ma' I Ma
S Mb Ma = I

Hence Mb Ma is a solution for S

Thanks! I'll give it a try!