I want to get the transformation matrix from the echelon form reduction 
over finite fields but I found in the SageMath documentation the following 
statement: 

*The matrix library used for Z/pZ/p-matrices does not return the 
transformation matrix, so the transformation option is ignored*

Link: 
http://doc.sagemath.org/html/en/reference/matrices/sage/matrix/matrix2.html#sage.matrix.matrix2.Matrix.echelon_form
 

More specifically, the call:  *M.echelon_form(transformation=True**) *does 
not return the transformation matrix T when M is over a finite field, only 
the echelon matrix E; T is such that we have T*M=E, so T is just the 
product of the elementary matrices, which perform the reducing row 
operations. 

Is there any workaround to get the transformation matrix T over a finite 
field? Can I get the transformation matrix T over ZZ and then reduce it 
over the finite field?

Any advice would be much appreciated.

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