TITLE: Is the identity matrix an elementary matrix?
QUESTION [5 upvotes]: My reasoning is yes, as you can switch row i with row i in the matrix... But I'm not sure if it's a "legal" elementary operation to switch a row with itself.

REPLY [4 votes]: This is a question of convention, but I would certainly consider the identity an elementary matrix, as I think most other mathematicians would. It corresponds to the elementary row operation of "doing nothing", which is about as simple as it gets.

REPLY [2 votes]: Sure, it fits very well as a row/column scaling operation scaling rows by 1, (but not really as a swapping operation.)