# What is the meaning of the row “opposite” the translation column?

Usually, I do my matrix multiplication like this:

[1 0 0 dx] | [px]   [px + dx]
[0 1 0 dy] | [py]   [py + dy]
[0 0 1 dz] | [pz] = [pz + dz]
[A B C  1] | [1]    [1]


Where the translation is along the right-hand edge of the matrix.

Once, I forgot about that and put them on the lower line instead, on the places marked as A B C above.

What did that do to the resulting points? With the upper-left 3x3 being an identity matrix, and the translation being zero, nothing happened to my point

[1 0 0 0] | [1]   [1]
[0 1 0 0] | [1]   [1]
[0 0 1 0] | [1] = [1]
[1 2 3 1] | [1]   [7]


except that 1 we always use in fourth place gets changed. Does this mean further multiplication with the point results in a mess? What am I doing by changing the bottom row?