How is a Elimination and Lower Triangluar Matrix related?

Question

Say for example I have a matrix,
$$ \begin{vmatrix} a&b&c\\ d&e&f\\ g&h&i\\ \end{vmatrix} $$
We can write a decomposistion for this matrix as: $\\A = LU$
Elimination matrix for this can be written like this: $\\EA = U$
I want to know is there a relation between 'E' and 'L' in this particular scenario, because my Professor is able to find it quite simply when talking about these.