Inverse of a symmetric matrix is not symmetric?

It works!

julia> s = Symmetric(mat)
6×6 Symmetric{Float64,Array{Float64,2}}:
 1.0          0.367879    0.0183156   0.00012341  1.12535e-7  1.38879e-11
 0.367879     1.0         0.367879    0.0183156   0.00012341  1.12535e-7 
 0.0183156    0.367879    1.0         0.367879    0.0183156   0.00012341 
 0.00012341   0.0183156   0.367879    1.0         0.367879    0.0183156  
 1.12535e-7   0.00012341  0.0183156   0.367879    1.0         0.367879   
 1.38879e-11  1.12535e-7  0.00012341  0.0183156   0.367879    1.0        

julia> inv(s)
6×6 Symmetric{Float64,Array{Float64,2}}:
  1.18147    -0.502645    0.1883     -0.0692716   0.0250252  -0.0079607
 -0.502645    1.39526    -0.582587    0.217304   -0.0786496   0.0250252
  0.1883     -0.582587    1.42474    -0.59216     0.217304   -0.0692716
 -0.0692716   0.217304   -0.59216     1.42474    -0.582587    0.1883   
  0.0250252  -0.0786496   0.217304   -0.582587    1.39526    -0.502645 
 -0.0079607   0.0250252  -0.0692716   0.1883     -0.502645    1.18147  

julia> issymmetric(inv(s))
true

Hooray for special matrix types!

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