(*Written by Matt Day (matthewd@uark.edu) as a demonstration for a linear algebra class*)

DynamicModule[{a1=1,a2=0,a3=0,b1=0,b2=1,b3=0,c1=0,c2=0,c3=1,A},{{{"a1",Slider[Dynamic[a1],{-3,3}]},{"a2",Slider[Dynamic[a2],{-3,3}]},{"a3",Slider[Dynamic[a3],{-3,3}]},{"b1",Slider[Dynamic[b1],{-3,3}]},{"b2",Slider[Dynamic[b2],{-3,3}]},{"b3",Slider[Dynamic[b3],{-3,3}]},{"c1",Slider[Dynamic[c1],{-3,3}]},{"c2",Slider[Dynamic[c2],{-3,3}]},{"c3",Slider[Dynamic[c3],{-3,3}]}},Dynamic[{A={{a1,a2,a3},{b1,b2,b3},{c1,c2,c3}};{MatrixForm[A],Det[A]},Graphics3D[{GeometricTransformation[Cuboid[{0,0,0},{1,1,1}],{A,{0,0,0}}]},Axes->True,PlotRange->{{-3,4},{-3,4},{-3,4}}]}]}]

DynamicModule[{a1=1,a2=0,a3=0,b1=0,b2=1,b3=0,c1=0,c2=0,c3=1,A},{{{"a1",Slider[Dynamic[a1],{-3,3}]},{"a2",Slider[Dynamic[a2],{-3,3}]},{"a3",Slider[Dynamic[a3],{-3,3}]},{"b1",Slider[Dynamic[b1],{-3,3}]},{"b2",Slider[Dynamic[b2],{-3,3}]},{"b3",Slider[Dynamic[b3],{-3,3}]},{"c1",Slider[Dynamic[c1],{-3,3}]},{"c2",Slider[Dynamic[c2],{-3,3}]},{"c3",Slider[Dynamic[c3],{-3,3}]}},Dynamic[{A={{a1,a2,a3},{b1,b2,b3},{c1,c2,c3}};{MatrixForm[A],Det[A]},Graphics3D[GeometricTransformation[{Cuboid[{0,0,0},{1,1,1/2}],Blue,Cuboid[{1/4,1/8,1/2},{1/2,7/8,5/8}],Cuboid[{1/2,5/8,1/2},{7/8,7/8,5/8}],Cuboid[{1/2,3/8,1/2},{5/8,1/2,5/8}]},{A,{0,0,0}}],Axes->True,PlotRange->{{-3,4},{-3,4},{-3,4}}]}]}]