Vertex
  v = (x, y)

Model object
  v0          v1
   +----------+
   |          |
   |          |
   |          |
   |          |
   +----------+
   v2         v3
 
Matrix
  M = [ a  b ]
      [ c  d ] 

Matrix times Vertex
  M * v = [ a  b ] * [ x ] = [ a*x + b*y ]
          [ c  d ]   [ y ]   [ c*x + d*y ]

Use the matrix to move the model.
  v0 = M*v0 // mutate the object referred to by v0, or replace the object referred to by v0?
  v1 = M*v1
  v2 = M*v2
  v3 = M*v3

for (int i = 0; i < model.vertexList.length; ++i)
  model.vertexList.set(i, M.times( model.vertexList.get(i) ); // replace the vertex

for (int i = 0; i < model.vertexList.length; ++i)
  model.vertexList.get(i).times( M );                         // mutate the vertex



start with a model and, translate it, rotate it, scale it, translate it
                           M1           M2        M3         M4


                                     1_000_000 vertices
for (int i = 0; i < model.vertexList.length; ++i)
{
  model.vertexList.get(i).times( M1 ); // mutate the vertex
  model.vertexList.get(i).times( M2 ); // mutate the vertex
  model.vertexList.get(i).times( M3 ); // mutate the vertex
  model.vertexList.get(i).times( M4 ); // mutate the vertex
}
// 4_000_000 matrix multiplications


The above loop does the following to each vertex vi,
   vi = M4 * (M3 * (M2 * (M1 * vi)))
which can be replaced with
   vi = (M4 * M3 * M2 * M1) * vi     // matrix multiply is associative



Matrix M5 = M4 * M3 * M2 * M1;        1_000_000 vertices
for (int i = 0; i < model.vertexList.length; ++i)
{
  model.vertexList.get(i).times( M5 ); // mutate the vertex
}
// 1_000_003 matrix multiplications