preparation

tt1[a_, b_] := {{1, 0, 0}, {0, 1, 0}, {a, b, 1}}; 
    MatrixForm[tt1[a, b]]

rr1[θ_] := {{Cos[θ], Sin[θ], 
          0}, {-Sin[θ], Cos[θ], 0}, {0, 0, 1}}; 
    MatrixForm[rr1[θ]]

ss1[a_, b_] := {{a, 0, 0}, {0, b, 0}, {0, 0, 1}}; 
    MatrixForm[ss1[a, b]]

mm1[n_] := 
        DiagonalMatrix[
          If[n == 1, {1, -1, 1}, {-1, 1, 
              1}]];
MatrixForm[mm1[1]]
MatrixForm[mm1[2]]

example 10.5   p.245

para = {x1 -> 2, 
        y1 -> 1}     
{x2, y2, one} = {x1, y1, 1} . tt1[4, 7] . mm1[2] . rr1[90  °] /. 
        para

example 10.6   p.245

para = {x1 -> 3, 
        y1 -> 6}    
{x2, y2, 
        one} = {x1, y1, 1} . tt1[0, -2] . rr1[90  °] . tt1[0, 2] /. 
        para