I have 3D cube and I need to do linear transformation on it: rotation by 45 degrees, Reflection in the x2-axis, A Contraction, A Dilation, A Vertical Expansion, A Shear.

   vtc = {{0, 0}, {1, 0}, {1, 1}, {0, 1}};(VertexTextureCoordinates)

    kocka = {{{0, 0, 0}, {0, 1, 0}, {1, 1, 0}, {1, 0, 0}}, {{0, 0, 0}, {1, 0, 0}, {1, 0, 1}, 
{0, 0, 1}}, {{1, 0, 0}, {1, 1, 0}, {1, 1, 1}, {1, 0, 1}}, {{1, 1, 0}, {0, 1, 0}, {0, 1, 1}, 
{1, 1, 1}}, {{0, 1, 0}, {0, 0, 0}, {0, 0, 1}, {0, 1, 1}}, {{0, 0, 1}, {1, 0, 1}, {1, 1, 1}, {0, 1, 1}}};

    MatrixForm[kocka] 

    Graphics3D[ Table[{Texture[mat[k]], Polygon[kocka[[k]], VertexTextureCoordinates -> vtc]}, {k, 1, 6}], 
Axes -> True, AxesLabel -> {x, y, z}, PlotRange -> 1]

So now I need to transpose the matrix and do the linear transformation on it.

**If you have any different examples on doing Linear Transformations of R^3 please, I will be very very grateful.

Thank you in advance.