Print["The matrix transformation is: ",MatrixForm[A = {{1,1},{6,0}}]];

graph = Plot[,{x,-10,10},PlotRange->{-10,10},AspectRatio->.9];
Avector = Graphics[{Thick,Red,Arrow[{{0,0},{2,2}}]}];
Bvector = Graphics[{Thick,Red,Arrow[{{0,0},{1,2}}]}];
Cvector = Graphics[{Thick,Red,Arrow[{{0,0},{1,0}}]}];
Dvector = Graphics[{Thick,Red,Arrow[{{0,0},{0,1}}]}];
Evector = Graphics[{Thick,Red,Arrow[{{0,0},{-2,-1}}]}];
Fvector = Graphics[{Thick,Red,Arrow[{{0,0},{-1,-2}}]}];

AImageVector = Graphics[{Thick,Green,Arrow[{{0,0},A.{2,2}}]}];
BImageVector = Graphics[{Thick,Green,Arrow[{{0,0},A.{1,2}}]}];
CImageVector = Graphics[{Thick,Green,Arrow[{{0,0},A.{1,0}}]}];
DImageVector = Graphics[{Thick,Green,Arrow[{{0,0},A.{0,1}}]}];
EImageVector = Graphics[{Thick,Green,Arrow[{{0,0},A.{-2,-1}}]}];
FImageVector = Graphics[{Thick,Green,Arrow[{{0,0},A.{-1,-2}}]}];

Show[graph, Avector,AImageVector]
Show[graph, Bvector,BImageVector]
Show[graph, Cvector,CImageVector]
Show[graph, Dvector,DImageVector]
Show[graph, Evector,EImageVector]
Show[graph, Fvector,FImageVector]