Do you think that it is possible to form a product that looks like this: 

Col. Matrix  x  Matrix   =   Result

  2 x 1         2 x 2    =    ???

A good answer might be:

No, this is not possible

Column Matrix on the Right, only

When a rectangular matrix and a column matrix are multiplied together, the column matrix will always be on the right of the rectangular matrix. It is only possible to multiply the two if they are conformant. Two matrices are conformant if the "inner dimension" of the each matrix is equal: 

Matrix      x     Column Matrix   =   Result

N x M              M x 1          =   N x 1
    ----------------
    inner dimensions
       are equal

QUESTION 4:

Do you think that it is possible to form a product that looks like this: 

Row Matrix  x  Col. Matrix   =   Scalar

1 x 2            2 x 1       =   1 x 1