### 2.32.7 Row reduction to echelon form in ℤ/pℤ : `Rref`

`Rref` is the inert form of `rref`.
`Rref` returns `rref` without evaluation. It is used in conjonction with `mod` in Maple syntax mode to find the row reduction to echelon form of a matrix with coefficients in ℤ/pℤ (see also 2.52.3).
Example, solve in ℤ/13ℤ

⎧ ⎨ ⎩ |
x + 2 · y | = | 9
3 · x +10 · y | = | 0

Input in `Xcas` mode :

`Rref([[1,2,9] mod 13,[3,10,0] mod 13])`

Output :

`rref([[1%13, 2%13, 9%13],[3%13,10%13,0%13]])`

you need to `eval(ans())` to get :

`[[1%13,0%13,3%13],[0%13,1%13,3%13]]`

and conclude that `x=3%13` and `y=3%13`.
Input in `Maple` mode :

`Rref([[1,2,9],[3,10,0],[3,11,1]]) mod 13`

Output :

`[[1,0,0],[0,1,0],[0,0,1]]`