MATLAB: Order of Addition changes answer? Approx 0 or actually 0

MATLABprecision

I've been trying to figure out for half a day why my Solution was not 0 by an order of 1.0e-14 or e-15. When I added several matrices together I noticed that the order to which I add them changes the value. Sol_1=0 (3X3) Matrix but Sol_2=~0(3X3). Please help, I can't figure it out.
clear
E1=80.32
E2=5.590
v12=0.338
G12=3.590
Composite_Properties=[E1 E2 v12 G12 0 0.254;
    E1 E2 v12 G12 -45 0.254;
    E1 E2 v12 G12 45 0.254;
    E1 E2 v12 G12 45 0.254;
    E1 E2 v12 G12 -45 0.254;
    E1 E2 v12 G12 0 0.254]
[r,c]=size(Composite_Properties)
    A=cell(1,r)
for i = 1:r
    A{i}=Q_BAR(Composite_Properties(i,1),Composite_Properties(i,2),Composite_Properties(i,3),Composite_Properties(i,4),Composite_Properties(i,5))*Composite_Properties(i,6)
end
A_SUM=A{1};
for i=2:(c)
    A_SUM=A_SUM+A{i};
end
    A_SUM
   z_k_bar=zeros(1,r,'double')
   for j=1:r
       z_k_bar(j)=(((-r/2)+((2*j-1)/2))*Composite_Properties(j,6))
   end
clear i j 
%Making B Matices
B=cell(1,r)
for i = 1:r
B{i}=Q_BAR(Composite_Properties(i,1),Composite_Properties(i,2),Composite_Properties(i,3),Composite_Properties(i,4),Composite_Properties(i,5))*z_k_bar(1,i)*Composite_Properties(i,6)
end
%Summation of B Matrices
 B_SUM=B{1}
for j=2:c
B_SUM=B_SUM + B{j};
end
B_SUM
Sol_1=B{1}+B{6}+B{2}+B{5}+B{3}+B{4} %0 Matrix%
Sol_2=B{1}+B{2}+B{3}+B{4}+B{5}+B{6}  %not Zero why???%

Best Answer

You can make some small changes for higher accuracy if you have the Symbolic Toolbox. Modified version enclosed.
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