Topology of a 2x2 Hamilton's matrix- need proof help

I would like to introduce the topology as the use of function in
geometry. Any function as geometric relation appears to be solvable
as topological set. A set corresponds abstracted. And to make the
set relation for Hamilton's matrix was the goal.

Here is the topology of a 2x2 matrix of Hamilton's form.


| a1 a2|
|b1 b2| = 1

An operatation as transform was to be utilized as the basis for
relative topology set.
A function.


1= |A1|^2 +|B2|^2

A solution begins the analysis. A1 as the element abstracts to
topological set corresponds as the number of a1 abstracted to number
equated as A1.

A magnitude as scalar always equates.


To prove this take all functions where a1 a2 and b1 b2 define
coefficients of homogneouos linear differential equations.

I pick a simple example to run through the matrix on.

0= a1*D +a2*D' And i refuse to do this type of integral. BUt all
function may be represented.

Given this a simple element transform was introduced to assist.


And this implies

|A1|^2+|B2|^2 = |h|

SO I have take a transform as the solution. And this is the method I
use for I do not apply theorem. I use this in quantum theory sombeody
else needs to formula the topology theory.

My tyransfomr is correct. But I need proof help.
Any Ideas?


Thanks in advance.

.