## Proving that a matrix is invertible

Hi,

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:

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,
otownsend