Hi @Bio_J,
To answer the first question:
Say for example you have the transformation matrix M of the general form:
\left(\begin{array}{cc}
a & b\\
c & d
\end{array}\right)
and vector v:
\left(\begin{array}{cc}
x\\
y
\end{array}\right)
If you do M * v, you would get:
\left(\begin{array}{cc}
a & b\\
c & d
\end{array}\right)
\left(\begin{array}{cc}
x\\
y
\end{array}\right)
=
\left(\begin{array}{cc}
ax + by\\
cx + dy
\end{array}\right)
If you do v * M (after reshaping v so matrix multiplication is valid), you would get:
\left(\begin{array}{cc}
x & y\\
\end{array}\right)
\left(\begin{array}{cc}
a & b\\
c & d
\end{array}\right)
=
\left(\begin{array}{cc}
ax + cy & bx + dy
\end{array}\right)
So these would not be equal. In your example matrix, it seems to have given the same result since b and c were both equal to 2, but that is not always true.
For your second question, I think that is incorrect because the value of the vector v[0] and v[1] can change depending on what you set v to be. The values in the transformation matrix needs to be constant, and must not depend on the v itself.
I hope this helps!