Transform M into row reduced echelon form (rref)
Gauss-Jordan Elimination
Mark first row (*) as next result row
M = * 00000000000000000000000000000001
Done.
M = 00000000000000000000000000000001
See also:
http://pages.pacificcoast.net/~cazelais/251/gauss-jordan.pdf
http://matrix.reshish.com/gauss-jordanElimination.php