diff --git a/Project.toml b/Project.toml
index 562430172..8eb6e4a35 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,6 +1,6 @@
 name = "ChainRules"
 uuid = "082447d4-558c-5d27-93f4-14fc19e9eca2"
-version = "0.7.32"
+version = "0.7.33"
 
 [deps]
 ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
diff --git a/src/rulesets/Base/arraymath.jl b/src/rulesets/Base/arraymath.jl
index e8eae0acc..023ccf7f4 100644
--- a/src/rulesets/Base/arraymath.jl
+++ b/src/rulesets/Base/arraymath.jl
@@ -21,8 +21,8 @@ end
 
 function rrule(
     ::typeof(*),
-    A::AbstractMatrix{<:CommutativeMulNumber},
-    B::AbstractMatrix{<:CommutativeMulNumber},
+    A::AbstractVecOrMat{<:CommutativeMulNumber},
+    B::AbstractVecOrMat{<:CommutativeMulNumber},
 )
     function times_pullback(Ȳ)
         return (
@@ -40,6 +40,28 @@ function rrule(
     return A * B, times_pullback
 end
 
+function rrule(
+    ::typeof(*),
+    A::AbstractVector{<:CommutativeMulNumber},
+    B::AbstractMatrix{<:CommutativeMulNumber},
+)
+    function times_pullback(Ȳ)
+        @assert size(B, 1) === 1   # otherwise primal would have failed.
+        return (
+            NO_FIELDS,
+            InplaceableThunk(
+                @thunk(Ȳ * vec(B')),
+                X̄ -> mul!(X̄, Ȳ, vec(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::CommutativeMulNumber, B::AbstractArray{<:CommutativeMulNumber}
 )
diff --git a/test/rulesets/Base/arraymath.jl b/test/rulesets/Base/arraymath.jl
index 8bc996860..4c205e784 100644
--- a/test/rulesets/Base/arraymath.jl
+++ b/test/rulesets/Base/arraymath.jl
@@ -20,8 +20,20 @@
             rrule_test(*, ⋆(dims), ⋆₂(dims), ⋆₂())
         end
 
+        @testset "AbstractMatrix-AbstractVector n=$n, m=$m" for n in (2, 3), m in (4, 5)
+            @testset "Array" begin
+                rrule_test(*, ⋆(n), n ⋆₂ m, ⋆₂(m))
+            end
+        end
+
+        @testset "AbstractVector-AbstractMatrix n=$n, m=$m" for n in (2, 3), m in (4, 5)
+            @testset "Array" begin
+                rrule_test(*, n ⋆ m, ⋆₂(n), 1 ⋆₂ m)
+            end
+        end
+
         @testset "AbstractMatrix-AbstractMatrix" begin
-            @testset "n=$n, m=$m, p=$p" for n in (2, 5), m in (2, 4), p in (2, 3)
+            @testset "Matrix * Matrix n=$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
@@ -46,6 +58,13 @@
                 end
             end
         end
+
+        @testset "Covector * Vector n=$n" for n in (3, 5)
+            @testset "$f" for f in (adjoint, transpose)
+                # This should be same as dot product and give a scalar
+                rrule_test(*, ⋆(), f.(⋆₂(n)), ⋆₂(n))
+            end
+        end
     end