Matrices, matrices and matrices

In Linear Algebra,
the rows of a matrix can be viewed as vectors.

So the interesting things come after such a brilliant idea.

Let's see a 2x2 matrix, M

in Latex: \left(\begin{array}{cc}3 & 2\\2 & -1\end{array}\right)

so there are two vectors <3,2> & <2,-1> in a 2-D space

given
what happens after sigma 1 times M is that M still is M!


So it is reasonable to regard sigma 1 as "one".

Besides, there are many other functional matrices,
Like, such a matrix makes another matrice upsidedown




so an interesting question comes:

WHY and HOW?