I hope someone can help. I'm suppose to prove that 5A is an invertible matrix, given that A is an invertible matrix. Here is the proof from my textbook:
Proving that a matrix is invertible-screen-shot-2017-12-03-11.44.11-am.png

I don't quite understand this proof, and so it would be great if someone could explain it to me. The specific part that I don't understand is why (5A)(1/5C) = (5)(1/5)(AC) = 1.

Let me know,