Integrating matrix minors without a loop

I am trying to integrate all the 2x2 matrices A(i-1:1,j-1:j) without using a loop. Right now I am doing in a loop but it is extremely slow. The code is shown below:

A=rand(500);
t=linspace(0,1,500);
for i=2:length(A)
   for j=2:length(A)
       A_minor=A(i-1:i,j-1:j);
       B(i,j)=trapz(t(j-1:j),trapz(t(i-1:i),A_minor));
   end
end