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Applying RREF transformation of one matrix to another

Given a matrix M, let M' be the matrix created by M.rref() Let E be a matrix made from composing the elementary row operations which took M to M.rref(). In particular, E satisfies M.rref() = EM I now wish to compute E (actually, EA, for any matrix A of the right dimension). Does Sagemath offer anything which allows me to bypass manually computing E?

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?