diff --git a/ext/FillArraysPDMatsExt.jl b/ext/FillArraysPDMatsExt.jl
index d5a0892d..0f98f775 100644
--- a/ext/FillArraysPDMatsExt.jl
+++ b/ext/FillArraysPDMatsExt.jl
@@ -3,10 +3,16 @@ module FillArraysPDMatsExt
 import FillArrays
 import FillArrays.LinearAlgebra
 import PDMats
+using FillArrays: mult_zeros, AbstractZeros
+using PDMats: ScalMat
 
 function PDMats.AbstractPDMat(a::LinearAlgebra.Diagonal{T,<:FillArrays.AbstractFill{T,1}}) where {T<:Real}
     dim = size(a, 1)
-    return PDMats.ScalMat(dim, FillArrays.getindex_value(a.diag))
+    return ScalMat(dim, FillArrays.getindex_value(a.diag))
 end
 
+Base.:*(a::ScalMat, b::AbstractZeros{T, 1} where T) = mult_zeros(a, b)
+Base.:*(a::ScalMat, b::AbstractZeros{T, 2} where T) = mult_zeros(a, b)
+Base.:*(a::AbstractZeros{T, 2} where T, b::ScalMat) = mult_zeros(a, b) # This is implemented in case ScalMat implements right multiplication
+
 end # module
diff --git a/test/runtests.jl b/test/runtests.jl
index 088089d4..32cd2ed7 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -2990,6 +2990,11 @@ end
         @test a.dim == length(diag)
         @test a.value == first(diag)
     end
+    a = ScalMat(4, 1.)
+    for zero in (Zeros(4), Zeros(4,4))
+        @test a * zero === zero
+    end
+    @test Zeros(4,4) * a === Zeros(4,4)
 end
 
 @testset "isbanded/isdiag" begin