diff --git a/src/dispatch.jl b/src/dispatch.jl
index c1f4cf43..20f98e36 100644
--- a/src/dispatch.jl
+++ b/src/dispatch.jl
@@ -474,26 +474,27 @@ Base.:*(A::AbstractArray, α::AbstractMutable) = A .* α
 
 # Needed for Julia v1.0, otherwise, `broadcast(*, α, A)` gives a `Array` and
 # not a `Symmetric`.
+
+_mult_upper(α, A) = parent(α * LinearAlgebra.UpperTriangular(parent(A)))
+_mult_lower(α, A) = parent(α * LinearAlgebra.LowerTriangular(parent(A)))
+
 function Base.:*(α::Number, A::LinearAlgebra.Symmetric{<:AbstractMutable})
-    return LinearAlgebra.Symmetric(
-        α * parent(A),
-        LinearAlgebra.sym_uplo(A.uplo),
-    )
+    c = LinearAlgebra.sym_uplo(A.uplo)
+    B = c == :U ? _mult_upper(α, A) : _mult_lower(α, A)
+    return LinearAlgebra.Symmetric(B, c)
 end
 
 function Base.:*(α::Number, A::LinearAlgebra.Hermitian{<:AbstractMutable})
-    return LinearAlgebra.Hermitian(
-        α * parent(A),
-        LinearAlgebra.sym_uplo(A.uplo),
-    )
+    c = LinearAlgebra.sym_uplo(A.uplo)
+    B = c == :U ? _mult_upper(α, A) : _mult_lower(α, A)
+    return LinearAlgebra.Hermitian(B, c)
 end
 
 # Fix ambiguity identified by Aqua.jl.
 function Base.:*(α::Real, A::LinearAlgebra.Hermitian{<:AbstractMutable})
-    return LinearAlgebra.Hermitian(
-        α * parent(A),
-        LinearAlgebra.sym_uplo(A.uplo),
-    )
+    c = LinearAlgebra.sym_uplo(A.uplo)
+    B = c == :U ? _mult_upper(α, A) : _mult_lower(α, A)
+    return LinearAlgebra.Hermitian(B, c)
 end
 
 # These three have specific methods that just redirect to `Matrix{T}` which