diff --git a/src/matmul.jl b/src/matmul.jl
index 2b2f7d81..d618bcfe 100644
--- a/src/matmul.jl
+++ b/src/matmul.jl
@@ -1072,11 +1072,13 @@ function __generic_matvecmul!(::typeof(identity), C::AbstractVector, A::Abstract
                 C[i] = zero(A[i]*B[1] + A[i]*B[1])
             end
         end
-        for k = eachindex(B)
-            aoffs = (k-1)*Astride
-            b = @stable_muladdmul MulAddMul(alpha,false)(B[k])
-            for i = eachindex(C)
-                C[i] += A[aoffs + i] * b
+        if !iszero(alpha)
+            for k = eachindex(B)
+                aoffs = (k-1)*Astride
+                b = @stable_muladdmul MulAddMul(alpha,false)(B[k])
+                for i = eachindex(C)
+                    C[i] += A[aoffs + i] * b
+                end
             end
         end
     end
diff --git a/test/matmul.jl b/test/matmul.jl
index c2ce312f..1fcf2009 100644
--- a/test/matmul.jl
+++ b/test/matmul.jl
@@ -980,11 +980,23 @@ Base.:*(x::Float64, a::A32092) = x * a.x
 end
 
 @testset "strong zero" begin
-    @testset for α in Any[false, 0.0, 0], n in 1:4
-        C = ones(n, n)
-        A = fill!(zeros(n, n), NaN)
-        B = ones(n, n)
+    @testset for α in Any[false, 0.0, 0], n in 1:4, T in (Float16, Float64)
+        C = ones(T, n)
+        A = fill(T(NaN), n, n)
+        B = ones(T, n)
         @test mul!(copy(C), A, B, α, 1.0) == C
+        C = ones(T, n, n)
+        B = ones(T, n, n)
+        @test mul!(copy(C), A, B, α, 1.0) == C
+    end
+    @testset for α in Any[false, 0.0, 0], β in Any[false, 0.0, 0], n in 1:4, T in (Float16, Float64)
+        C = fill(T(NaN), n)
+        A = fill(T(NaN), n, n)
+        B = fill(T(NaN), n)
+        @test iszero(mul!(copy(C), A, B, α, β))
+        C = fill(T(NaN), n, n)
+        B = fill(T(NaN), n, n)
+        @test iszero(mul!(copy(C), A, B, α, β))
     end
 end