Understanding a question in combinatorics

Question

I need help to understand a question in combinatorics.

One corner square in a $3 \times 3$ grid is painted black, the other squares are white. In one move you can change color in all squares in a row or in a column. Can you get all the squares black after a number of such moves?

Hint: Study the number of black squares among the four corner squares

Does this regard a Rubiks cube? I cannot see other option that that, given the expression "in one move".

If not, any hints appreciated!

[[ Not looking for Solutions , only want Clarification on the Question ]]

Answer 1

It is a Planar Puzzle , not a Cubic Puzzle (Definitely not Rubic)

Putting in other words & Using Images may aid here , hence I will try that :

We have a 3×3 grid like given below  
One Corner Square in that is Initially painted Black.  
The other Squares are left White.  
Playing a game , you have 2 Possible moves :  
- you can change the colour in all Squares in a Selected row.  
- you can change the colour in all Squares in a Selected column.  

Aim of the game is to make the grid all Black.  
You can use these 2 moves in Succession.  
Can you get all the Squares Black after a number of such moves ?  
What is the Sequence of moves ?  

Hint: Study the number of Black Squares among the four corner Squares  

No Colouring :

Starting Position :

Playing with the move to the top row :

Ending Position :

Solution :

Not Posting the Puzzle Solution.  
OP wants Puzzle Explanation , not Puzzle Solution.  

When OP responds , I may include that here.  

My HINT : There is Some Invariant which we can try to Identify.  
That Invariant will not change when making the moves.  
That Invariant is not there in the Ending Position.  

Answer 2

Starting sequence:

[X][][]
[][][]
[][][]

...

Target sequence:

[X][X][X]
[X][X][X]
[X][X][X]

Solution:

I think it is unsolvable as the starting position is already in a non-solvable state. It represents a planar graph.

Prem's hint: Study the number of Black Squares among the four corner Squares

There is only 1 black square as a corner, it isn't solvable because of this principle.

Prem's hint 2: There is Some Invariant which we can try to Identify.

Prem's hint 3: That Invariant will not change when making the moves.

Prem's hint 4: That Invariant is not there in the Ending Position.

The upper left square is what is invariant, it will inevitably transform into a white square.