Representation of linear transformation of matrix

Let say there is a 3x3 matrix

[m11 m12 m13]

[m21 m22 m23]

[m31 m32 m33]

[m11 m12 m13] is a row vector

[m21 m22 m23] is a row vector

[m31 m32 m33] is a row vector

and which of above are basis vectors in 3D space. i, j, k in standard form.

[m11 m12 m13] is a row vector and i

[m21 m22 m23] is a row vector and j

[m31 m32 m33] is a row vector and k

using linear transformation we can write a vector v like down below.

v = vx*i + vy*j + vz*k

if we apply some transform(matrix) into vector V and we can visualize it.

for instance we have 

[1 0 0]

[0 1 0] == matrix A

[0 0 1]

it is an identity matrix and if we multiply vector v with matrix.

vA

we will get v because A is an identity matrix.

if matrix A is like down below.

[0.75 0.75 0]

[0 1 0]

[0 0 1]

vector v or shape of model will be scaled, shrink.

Using this representation, we can guess what the shape will look like when we apply some transformations. (Sorry! I'm not good at drawing)