A = randn(2,2); %random matrix, Gaussian sampling
I = eye(2,2);
N = 500;
alpha = 0:2*pi/N:2*pi; %cut 2pi into N pieces

U = [cos(alpha); sin(alpha)]; % unit circle
resultA = A*U; %transforming unit circle by matrix A
resultI = I*U; %ditto for I

xA = resultA(1,:); yA = resultA(2,:); %splits results into components
xI = resultI(1,:); yI= resultI(2,:);

hold off;
plot(xA,yA,'r','LineWidth', 2);
hold on;axis equal
plot(xI,yI,'b','LineWidth', 2);

M = 50;
alpha = 0:2*pi/M:2*pi; %cut 2pi into M pieces
U = [cos(alpha); sin(alpha)];
resultA = A*U;
for i=1:M %plot pairs of points on circle and A*circle
    plot([U(1,i) resultA(1,i)],[U(2,i) resultA(2,i)], 'k','LineWidth',1);
end