2 x 2 matrix division

A 2 x 2 matrix A multiplied by a 2 x 2 matrix B is a 2 x 2 matrix AB. This tool helps to find the inverse of matrix B so that we can find out what matrix A is.

Multiplication of a matrix:

(1)
\begin{align} \left(\ \begin{matrix} a & b \\ c & d \end{matrix}\right) \left(\ \begin{matrix} e & f \\ g & h \end{matrix}\right) = \left(\ \begin{matrix} ae+bg & af+bh \\ ce+dg & cf+dh \end{matrix}\right) = \left(\ \begin{matrix} i & j \\ k & l \end{matrix}\right) \end{align}

So when you divide one matrix by another, you have to solve some equations.

// Warning! This code may be inaccurate in syntax or may not work properly.
// Please refrain from using it.
function divide2x2matrix(e,f,g,h,i,j,k,l)
/**
*We assume that the matrix is in the form [[i,j],[k,l]] and [[e,f],[g,h]].
*The first bracket  is the upper row, second bracket lower row.
*Matrix returned: [[a,b],[c,d]]
*/
/**
*The first step is to solve the simultaneous equations.
*The simultaneous equations are:
*ae+bg=i }
*af+bh=j }focus on these first
*ce+dg=k }
*cf+dh=l }then focus on these
*aeh+bgh=hi
*afg+bgh=gj
*=>aeh-afg=hi-gj
*=>a=(hi-gj)/(eh-fg)
*=>aef+bfg=fi
*=>aef+beh=ej
*=>bfg-beh=fi-ej
*=>b=(fi-ej)/(fg-eh)
*Using the same method:
*ce+dg=k
*cf+dh=l
*c=(kh-lg)/(eh-fg)
*d=(fk-el)/(fg-eh)
*/
var discrim=(e*h-g*f)
if (discrim!=0) {
a=(h*i-g*j);
a/=discrim;
b=(e*j-f*i);
b/=discrim;
c=(k*h-l*g);
c/=discrim;
d=(e*l-f*k);
d/=discrim;
return a,b,c,d;
}
else {