inv(::Cholesky) always symmetric

src/cholesky.jl

@@ -70,7 +70,8 @@ end
 LinearAlgebra.hermitian_type(::Type{SA}) where {T, S, SA<:SArray{S,T}} = Hermitian{T,SA}
 
 function inv(A::Cholesky{T,<:StaticMatrix{N,N,T}}) where {N,T}
-    return A.U \ (A.U' \ SDiagonal{N}(I))
+    B = A.U \ (A.U' \ SDiagonal{N}(I))
+    return (B .+ B') ./ T(2)
 end
 
 function Base.:\(A::Cholesky{T,<:StaticMatrix{N,N,T}}, B::StaticVecOrMatLike) where {N,T}

test/chol.jl

@@ -57,6 +57,11 @@ using LinearAlgebra: PosDefException
             c = cholesky(m)
             @test (@inferred inv(c)) isa SMatrix{3,3,elty}
             @test inv(c) ≈ SMatrix{3,3}(inv(m_a))
+            # Check special case of 2 × 2 inverse that used to trigger an
+            # error
+            c2 = cholesky(@SMatrix elty[π 3.1; 3.1 12.0])
+            d2 = inv(c2)
+            @test d2[1,2] == d2[2,1]
         end
 
         @testset "Division" begin