A = {{1, 3, 
            1}, {2, -1, -3}, {1, 1, -2}};

    (a);

    Print["A=", A // MatrixForm];

(b);
  

<< LinearAlgebra`MatrixManipulation`
Aaugment = 
        AppendRows[A, IdentityMatrix[3]];
Print["Aaugment=", 
        Aaugment // MatrixForm];
RowReduceAaugment = RowReduce[Aaugment];
Print["RowReduce[Aaugment]=", 
        RowReduceAaugment // MatrixForm];
Right3columns = 
TakeColumns[
          RowReduceAaugment, -3];
Print["Right3columns=", 
        Right3columns // MatrixForm];

\(\(\( (*We\ can\ check\ the\ above\ result*) \)\(
\)\(\(Print["Right3colomns.A=", 
        Right3columns . A // MatrixForm];\)\(
\)
    \)\)\)