### Applying RREF transformation of one matrix to another

Given a matrix ~~M, ~~`M`

, let ~~M' ~~`M'`

be the matrix created by ~~M.rref()
~~`M.rref()`

.
Let ~~E ~~`E`

be a matrix made from composing the elementary row operations which took ~~M ~~`M`

to ~~M.rref(). ~~`M.rref()`

. In particular, E satisfies

`M.rref() = `~~EM
~~EM

.

I now wish to compute ~~E ~~`E`

(actually, ~~EA, ~~`EA`

, for any matrix ~~A ~~`A`

of the right dimension). Does Sagemath offer anything which allows me to bypass manually computing ~~E?~~`E`

?