Matrix A:    
        (a11) (a12)
  x2 - y2 = detA= (a21) (a22)
  xy       = MatrixB=√A: (b11) (b12)
  Find out   DetB= (b21) (b22)
           
  x2(1) y2(1)  
  x(11)= y(11)=  
  x(12)= y(12)=  
           
  x2(2) y2(2)  
  x(21)= i y(21)= i  
  x(22)= i y(22)= i  
           
 

* x2 - y2 =(√a)2 is the equation of a rectangular hyperbola. Rectangular hyperbola is one whose transverse (major axis in ellipse) and conjugate axis (minor axis in ellipse) are of equal length( similar to circle) .

* xy=(√b)2  is another equation of rectangular hyperbola where the co-ordinate axes are rotated through 45 degree without changing the origin. Hence all the pairs of (x,y) represent the points of intersection of two hyperbolas.