inverse of symmetric matrix is not guaranteed to be symmetric

[imLew]

Is this the right place for issues with LinearAlgebra.jl
Here is an MWE

while true
    R = randn((3,3))
    R[2,1] = R[1,2]; R[3,1] = R[1,3]; R[2,3]=R[3,2]
    @assert R == R'
    @assert inv(R) == inv(R)'
end

[imLew]

I learned that the way to deal with this is to tell inv() that it is a symmetric matrix by passing it to Symmetric() first.
This was an annoying bug to hunt down so I'm inclined to suggest the inv() function should check for symmetry, but then again I don't know how much overhead that would introduce.