hi sharan

with (plots, implicitplot):
    a := A[1,1] + 1:
    b := A[1,2]:
    c := A[2,1]:
    d := A[2,2] + 1:
    ellipse := (c^2+d^2)*x^2 - 2*(a*c + b*d)*x*y + (a^2+b^2)*y^2 = (a*d-b*c)^2 :
    print (ellipse);
    Z := implicitplot(ellipse, x=-10..10, y=-10..10, scaling=constrained, gridrefine=2);