diff --git a/Project.toml b/Project.toml
index 22c18a54b..96ed5692d 100644
--- a/Project.toml
+++ b/Project.toml
@@ -4,6 +4,7 @@ version = "0.7.27"
 
 [deps]
 ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
+Compat = "34da2185-b29b-5c13-b0c7-acf172513d20"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 Reexport = "189a3867-3050-52da-a836-e630ba90ab69"
@@ -21,7 +22,6 @@ julia = "1"
 
 [extras]
 ChainRulesTestUtils = "cdddcdb0-9152-4a09-a978-84456f9df70a"
-Compat = "34da2185-b29b-5c13-b0c7-acf172513d20"
 FiniteDifferences = "26cc04aa-876d-5657-8c51-4c34ba976000"
 NaNMath = "77ba4419-2d1f-58cd-9bb1-8ffee604a2e3"
 Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
@@ -29,4 +29,4 @@ SpecialFunctions = "276daf66-3868-5448-9aa4-cd146d93841b"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 
 [targets]
-test = ["ChainRulesTestUtils", "Compat", "FiniteDifferences", "NaNMath", "Random", "SpecialFunctions", "Test"]
+test = ["ChainRulesTestUtils", "FiniteDifferences", "NaNMath", "Random", "SpecialFunctions", "Test"]
diff --git a/src/ChainRules.jl b/src/ChainRules.jl
index 1e0989b40..279291ab3 100644
--- a/src/ChainRules.jl
+++ b/src/ChainRules.jl
@@ -4,6 +4,7 @@ using Reexport
 @reexport using ChainRulesCore
 
 using Base.Broadcast: materialize, materialize!, broadcasted, Broadcasted, broadcastable
+using Compat
 using LinearAlgebra
 using LinearAlgebra.BLAS
 using Random
diff --git a/src/rulesets/Base/arraymath.jl b/src/rulesets/Base/arraymath.jl
index da81a9b61..fd2457f01 100644
--- a/src/rulesets/Base/arraymath.jl
+++ b/src/rulesets/Base/arraymath.jl
@@ -19,23 +19,47 @@ end
 ##### `*`
 #####
 
-function rrule(::typeof(*), A::AbstractMatrix{<:Real}, B::AbstractMatrix{<:Real})
+function rrule(::typeof(*), A::AbstractMatrix{<:Number}, B::AbstractMatrix{<:Number})
     function times_pullback(Ȳ)
-        return (NO_FIELDS, @thunk(Ȳ * B'), @thunk(A' * Ȳ))
+        return (
+            NO_FIELDS,
+            InplaceableThunk(
+                @thunk(Ȳ * B'),
+                X̄ -> mul!(X̄, Ȳ, B', true, true)
+            ),
+            InplaceableThunk(
+                @thunk(A' * Ȳ),
+                X̄ -> mul!(X̄, A', Ȳ, true, true)
+            )
+        )
     end
     return A * B, times_pullback
 end
 
-function rrule(::typeof(*), A::Real, B::AbstractArray{<:Real})
+function rrule(::typeof(*), A::Number, B::AbstractArray{<:Number})
     function times_pullback(Ȳ)
-        return (NO_FIELDS, @thunk(dot(Ȳ, B)), @thunk(A * Ȳ))
+        return (
+            NO_FIELDS,
+            @thunk(dot(Ȳ, B)'),
+            InplaceableThunk(
+                @thunk(A' * Ȳ),
+                X̄ -> mul!(X̄, conj(A), Ȳ, true, true)
+            )
+        )
     end
     return A * B, times_pullback
 end
 
-function rrule(::typeof(*), B::AbstractArray{<:Real}, A::Real)
+function rrule(::typeof(*), B::AbstractArray{<:Number}, A::Number)
     function times_pullback(Ȳ)
-        return (NO_FIELDS, @thunk(A * Ȳ), @thunk(dot(Ȳ, B)))
+        return (
+            NO_FIELDS,
+            InplaceableThunk(
+                @thunk(A' * Ȳ),
+                X̄ -> mul!(X̄, conj(A), Ȳ, true, true)
+            ),
+            @thunk(dot(Ȳ, B)'),
+        )
     end
     return A * B, times_pullback
 end
diff --git a/test/rulesets/Base/arraymath.jl b/test/rulesets/Base/arraymath.jl
index e12060966..1ec987d36 100644
--- a/test/rulesets/Base/arraymath.jl
+++ b/test/rulesets/Base/arraymath.jl
@@ -6,26 +6,50 @@
         rrule_test(inv, randn(T, N, N), (B, randn(T, N, N)))
     end
 
-    @testset "*" begin
-        @testset "Matrix-Matrix" begin
-            dims = [3,4,5]
-            for n in dims, m in dims, p in dims
-                # don't need to test square case multiple times
-                n > 3 && n == m == p && continue
-                A = randn(m, n)
-                B = randn(n, p)
-                Ȳ = randn(m, p)
-                rrule_test(*, Ȳ, (A, randn(m, n)), (B, randn(n, p)))
-            end
+    # TODO Test on Complex once we have Complex support for all of these.
+    @testset "*: $T" for T in (Float64, ComplexF64)
+        ⋆(a) = round.(5*randn(T, a))  # Helper to generate nice random values
+        ⋆(a, b) = ⋆((a, b))  # matrix
+        ⋆() = only(⋆(()))  # scalar
+
+        ⋆₂(a) = (⋆(a), ⋆(a)) # Helper to generate random matrix and its cotangent
+        ⋆₂(a, b) = ⋆₂((a, b))  #matrix
+        ⋆₂() = ⋆₂(())  # scalar
+
+        @testset "Scalar-Array $dims" for dims in ((3,), (5,4), (2, 3, 4, 5))
+            rrule_test(*, ⋆(dims), ⋆₂(), ⋆₂(dims))
+            rrule_test(*, ⋆(dims), ⋆₂(dims), ⋆₂())
         end
-        @testset "Scalar-AbstractArray" begin
-            for dims in ((3,), (5,4), (10,10), (2,3,4), (2,3,4,5))
-                rrule_test(*, randn(dims), (1.5, 4.2), (randn(dims), randn(dims)))
-                rrule_test(*, randn(dims), (randn(dims), randn(dims)), (1.5, 4.2))
+
+        @testset "AbstractMatrix-AbstractMatrix" begin
+            @testset "n=$n, m=$m, p=$p" for n in (2, 5), m in (2, 4), p in (2, 3)
+                @testset "Array" begin
+                    rrule_test(*, n⋆p, (n⋆₂m), (m⋆₂p))
+                end
+
+                @testset "SubArray - $indexname" for (indexname, m_index) in (
+                    ("fast", :), ("slow", Ref(m:-1:1))
+                )
+                    rrule_test(*, n⋆p, view.(n⋆₂m, :, m_index), view.(m⋆₂p, m_index, :))
+                    rrule_test(*, n⋆p, n⋆₂m, view.(m⋆₂p, m_index, :))
+                    rrule_test(*, n⋆p, view.(n⋆₂m, :, m_index), m⋆₂p)
+                end
+
+                @testset "Adjoints and Transposes" begin
+                    rrule_test(*, n⋆p, Transpose.(m⋆₂n), Transpose.(p⋆₂m))
+                    rrule_test(*, n⋆p, Adjoint.(m⋆₂n), Adjoint.(p⋆₂m))
+
+                    rrule_test(*, n⋆p, Transpose.(m⋆₂n), (m⋆₂p))
+                    rrule_test(*, n⋆p, Adjoint.(m⋆₂n), (m⋆₂p))
+
+                    rrule_test(*, n⋆p, (n⋆₂m), Transpose.(p⋆₂m))
+                    rrule_test(*, n⋆p, (n⋆₂m), Adjoint.(p⋆₂m))
+                end
             end
         end
     end
 
+
     @testset "$f" for f in (/, \)
         @testset "Matrix" begin
             for n in 3:5, m in 3:5