No. Column scrambling doesn't affect row ordering and row scrambling doesn't affect column ordering. They are literally orthogonal. You can't tell, from a scrambled matrix, whether the rows or the columns were scrambled first.

Here's a more explicit breakdown:

    (0,0) (1,0) (2,0)
    (0,1) (1,1) (2,1)
    (0,2) (1,2) (2,2)

Column scrambling: swap 1&2:

    (0,0) (2,0) (1,0)
    (0,1) (2,1) (1,1)
    (0,2) (2,2) (1,2)

Now row scrambling: swap 0&1:

    (0,1) (2,1) (1,1)
    (0,0) (2,0) (1,0)
    (0,2) (2,2) (1,2)

Notice how the x coordinates still all match along the vertical, and y coordinates still all match along the horizontal.

Let's try it in the other order, row first:

    (0,1) (1,1) (2,1)
    (0,0) (1,0) (2,0)
    (0,2) (1,2) (2,2)

And columns:

    (0,1) (2,1) (1,1)
    (0,0) (2,0) (1,0)
    (0,2) (2,2) (1,2)

It's the same result irrespective of the order.