How to do reduce rows with Wolfram Alpha over certain set

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If I want to row reduce a matrix:

$$ \begin{matrix} 1 & -1 & 0 & 4 \\ 2 & -2 & 1 & 3 \\ 5 & -5 & 1 & 15 \\ \end{matrix} $$

over $$\mathbb{Z}_3$$ is there a way I can do this in Wolfram Alpha? Thanks!

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Use the syntax I have written here, then reduce mod 3 manually.

I just typed:

RowReduce[{{1, -1, 0, 4}, {2, -2, 1, 3}, {5, -5, 1, 15}}]

As Amzoti points out well, and I just found out through test, WA just kinda burps on adding the Modulus->3 parameter.

Go to Wolfram Cloud, sign in to the "Wolfram Programming Cloud", and have your way with the Mathematica syntax. If you do it there, the statement

MatrixForm[
 RowReduce[{{1, -1, 0, 4}, {2, -2, 1, 3}, {5, -5, 1, 15}}, 
  Modulus -> 3]]

will give you that which you desire with no cost. :)