I’ve been struggling with this for some time. I can prove the Snake Lemma, but I don’t really “understand” it. By that I mean if no one told me Snake Lemma existed, I would not even attempt to prove it. I believe I am missing some important intuition that tells me that the lemma “could” be true before actually trying to prove it. Please give me some pointers.

**Answer**

All these diagram chasing lemmas (snake lemma, 3x3 lemma, four lemma, five lemma, etc.) follow directly from the “salamander lemma” due to George Bergman, see salamander lemma.

And *that* is pretty transparent. It is so transparent that for instance it is immediate to see (which no textbook ever mentions) that there are just as easily 4×4 lemmas, 5×5 lemmas, 6×6 lemmas. etc. In other words: once you see the simple idea of the salamander lemma, you can come up yourself with more such diagram chasing lemmas at will.

**Attribution***Source : Link , Question Author : Tunococ , Answer Author : Norbert*