Hi, billa. Thank you for your comments.
I think there is a little misunderstanding perhaps due to our different notation. I guess that your notation r1c5 stands for row 1 column 5, while in the coordinates notation we normally use in the site this corresponds to e1, that is, column e row 1 (as in the drawing provided by Patrick, certainly the curious thing is that with this notation we place first the column and secondly the row inversely to the algebra typical notation ).

But what I say in the reasoning is that this cell cannot be a 3 (and consequently e4 = 2) and I later demonstrate why. Of course, if e1 = 2 >>> e4 = 3, but this would have been impossible since we have a "6+" cage in cells c4-d4.
So, necessarily, e1 = 6 (and e4 = 1) in the final solution since the product of both cells is 6.

Happy new year too for you and your relatives.