I'm working through a tutorial on matrices: Pauls Online Notes : Linear Algebra - Finding Inverse Matrices

I'm confused about the following bit:

If is invertible then there are a set of elementry matrices such that . If we multiply both sides of this by :

I'm confused by that statement. I don't see how to get to isolate the inverse to obtain . On the left side of the arrow, I have , but I still don't see how this implies that (Headbang)