Numerical precision of matrix multiplication (inconsistent results with colon indexing)

Why do the two ways of matrix multiplication lead to different results?

 rng(1);
A = randn(100,3);
B = A'*A;
C = A(:,:)'*A(:,:);

 B-C

results in

 ans =

   1.0e-13 *

         0   -0.0178    0.0133
   -0.0178   -0.1421   -0.0133
    0.0133    0.0311    0.1421

The difference is not huge, but still I don't understand why the results differ at all.

Answer 1

[Jos (10584)]

Strange! Also strange:

rng(1) ; A = randn(100,3) ;
B1 = A'*A 
B2 = mtimes(A',A)  
disp(['B1 == B2 : ' '0'+isequal(B2, B1)]) ;  % ?????

% but

X = A' ;
C1 = X*A  
C2 = mtimes(X,A) 
disp(['C1 == C2 : ' '0'+isequal(C1, C2)]) ;   % YES!
disp(['C1,C2 == B2 : ' '0'+isequal(C1, C2, B2)]) ;

I first thought that your C is created using MTIMES:

C = A(:,:)'*A(:,:)
disp(['C == B2 : ' '0'+isequal(C, B2)]) ; % but no
disp(['C == B1 : ' '0'+isequal(C, B1)]) ; % also not!!

So there are at least three different results, that should be the same ...

Very puzzling!