The matrix which I get for Scaling , Shearing and Rotation are follows:
Scale:
Shear
Rotation 
Why do we need Homogenous Co-ordinate to get the transformation matrix as listed below? (need a example)
I am also confused with linear transformation , which you used with homogenous co-ordinate. As far as I know, linear in transformation the following must be satisfied.
- T(x+y)=T(x) + T(y)
- T(c.x)=cT(x) Where x and y are vector, and c is a constant.
How do I associate the concept with Affine Transformation. Please help to understand this concept.
You are missing the translation transformation that is indicated by the $t_x,t_y$ entries in your matrix. In the plane you have 4 degrees of freedom in linear transformations that leave the origin in place, and then again two degrees of freedom in shifting the origin.
Note that your convention to write the transformation matrix is contrary to the general mathematical use. Your points in the plane are encoded as row vectors $(p_x,p_y,1)$ and the matrix acts from the right,
$$[p,1]\cdot\begin{bmatrix}A&0\\t&1\end{bmatrix}=[pA+t,1]$$