symmetric matrix multiplication

I have a symmetric matrix B (17x17), and a (17x17) square matrix A.  If do
the following matrix multiplication I SHOULD get a symmetric matrix, however
i don't.  The computation required is:

C = t(A)%*%B%*%A

here are some checks for symmetry

(max(abs(B - t(B))))

[1] 0

C = t(A)%*%B%*%A
(max(abs(C - t(C))))

[1] 3.552714e-15

Any help on the matter would be very much appreciated.


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