A=(({{3/2, 1/2}, {1/2, 3/2}}));

a = {1, 0};
b = {0, 
          1};
anew = A . a;
bnew = 
        A . b;
firstgraph = 
        Show[Graphics[Line[{{0, 0}, a, a + b, b, {0, 0}}]], 
          Axes -> True, AspectRatio -> Automatic, 
          PlotRange -> {{-3, 3}, {-3, 3}}, 
          DisplayFunction -> Identity];
secondgraph = 
        Show[Graphics[Line[{{0, 0}, anew, anew + bnew, bnew, {0, 0}}]], 
          Axes -> True, AspectRatio -> Automatic, 
          PlotRange -> {{-3, 3}, {-3, 3}}, 
          DisplayFunction -> 
            Identity];
Print[" "];
Print["A = ", MatrixForm[A]];
Show[
        GraphicsArray[{firstgraph, secondgraph}]];