diff --git a/src/matmul.jl b/src/matmul.jl
index d618bcfe..311ddfcf 100644
--- a/src/matmul.jl
+++ b/src/matmul.jl
@@ -599,11 +599,17 @@ function generic_syrk!(C::StridedMatrix{T}, A::StridedVecOrMat{T}, conjugate::Bo
         throw(DimensionMismatch(lazy"output matrix has size: $(size(C)), but should have size $((mA, mA))"))
     end
 
-    _rmul_or_fill!(C, β)
+    if (!iszero(β) || isempty(A)) # return C*beta
+        _rmul_or_fill!(C, β)
+    else # iszero(β) && A is non-empty
+        aA_11 = abs2(A[1,1])
+        fill!(UpperTriangular(C), zero(aA_11 + aA_11))
+    end
+    iszero(α) && return C
     @inbounds if !conjugate
         if aat
             for k ∈ 1:n, j ∈ 1:m
-                αA_jk = A[j, k] * α
+                αA_jk = @stable_muladdmul MulAddMul(α, false)(A[j, k])
                 for i ∈ 1:j
                     C[i, j] += A[i, k] * αA_jk
                 end
@@ -614,17 +620,17 @@ function generic_syrk!(C::StridedMatrix{T}, A::StridedVecOrMat{T}, conjugate::Bo
                 for k ∈ 2:m
                     temp += A[k, i] * A[k, j]
                 end
-                C[i, j] += temp * α
+                C[i, j] += @stable_muladdmul MulAddMul(α, false)(temp)
             end
         end
     else
         if aat
             for k ∈ 1:n, j ∈ 1:m
-                αA_jk_bar = conj(A[j, k]) * α
+                αA_jk_bar = @stable_muladdmul MulAddMul(α, false)(conj(A[j, k]))
                 for i ∈ 1:j-1
                     C[i, j] += A[i, k] * αA_jk_bar
                 end
-                C[j, j] += abs2(A[j, k]) * α
+                C[j, j] += @stable_muladdmul MulAddMul(α, false)(abs2(A[j, k]))
             end
         else
             for j ∈ 1:n
@@ -633,13 +639,13 @@ function generic_syrk!(C::StridedMatrix{T}, A::StridedVecOrMat{T}, conjugate::Bo
                     for k ∈ 2:m
                         temp += conj(A[k, i]) * A[k, j]
                     end
-                    C[i, j] += temp * α
+                    C[i, j] += @stable_muladdmul MulAddMul(α, false)(temp)
                 end
                 temp = abs2(A[1, j])
                 for k ∈ 2:m
                     temp += abs2(A[k, j])
                 end
-                C[j, j] += temp * α
+                C[j, j] += @stable_muladdmul MulAddMul(α, false)(temp)
             end
         end
     end
@@ -1132,8 +1138,21 @@ __generic_matmatmul!(C, A, B, alpha, beta, ::Val{true}) = _generic_matmatmul_non
 __generic_matmatmul!(C, A, B, alpha, beta, ::Val{false}) = _generic_matmatmul_generic!(C, A, B, alpha, beta)
 
 function _generic_matmatmul_nonadjtrans!(C, A, B, alpha, beta)
-    _rmul_or_fill!(C, beta)
-    (iszero(alpha) || isempty(A) || isempty(B)) && return C
+    # _rmul_or_fill!(C, beta) spelled out more carefully to allow for zero-less eltypes
+    if (!iszero(beta) || isempty(A) || isempty(B)) # return C*beta
+        _rmul_or_fill!(C, beta)
+    else # iszero(beta) && A and B are non-empty
+        a1 = firstindex(A, 2)
+        b1 = firstindex(B, 1)
+        for j in axes(C, 2)
+            B_1j = B[b1, j]
+            for i in axes(C, 1)
+                C_ij = A[i, a1] * B_1j
+                C[i,j] = zero(C_ij + C_ij)
+            end
+        end
+    end
+    iszero(alpha) && return C
     @inbounds for n in axes(B, 2), k in axes(B, 1)
         # Balpha = B[k,n] * alpha, but we skip the multiplication in case isone(alpha)
         Balpha = @stable_muladdmul MulAddMul(alpha, false)(B[k,n])
@@ -1145,20 +1164,40 @@ function _generic_matmatmul_nonadjtrans!(C, A, B, alpha, beta)
     C
 end
 function _generic_matmatmul_adjtrans!(C, A, B, alpha, beta)
-    _rmul_or_fill!(C, beta)
-    (iszero(alpha) || isempty(A) || isempty(B)) && return C
     t = _wrapperop(A)
     pB = parent(B)
     pA = parent(A)
+    if (!iszero(beta) || isempty(A) || isempty(B)) # return C*beta
+        _rmul_or_fill!(C, beta)
+    else # iszero(beta) && A and B are non-empty
+        a1 = firstindex(pA, 1)
+        b1 = firstindex(pB, 2)
+        for j in axes(C, 2)
+            tB_1j = t(pB[j, b1])
+            for i in axes(C, 1)
+                C_ij = t(pA[a1, i]) * tB_1j
+                C[i,j] = zero(C_ij + C_ij)
+            end
+        end
+    end
+    iszero(alpha) && return C
     tmp = similar(C, axes(C, 2))
     ci = firstindex(C, 1)
     ta = t(alpha)
-    for i in axes(A, 1)
-        mul!(tmp, pB, view(pA, :, i))
-        @views C[ci,:] .+= t.(ta .* tmp)
-        ci += 1
+    if isone(ta)
+        for i in axes(A, 1)
+            mul!(tmp, pB, view(pA, :, i))
+            @views C[ci,:] .+= t.(tmp)
+            ci += 1
+        end
+    else
+        for i in axes(A, 1)
+            mul!(tmp, pB, view(pA, :, i))
+            @views C[ci,:] .+= t.(ta .* tmp)
+            ci += 1
+        end
     end
-    C
+    return C
 end
 function _generic_matmatmul_generic!(C, A, B, alpha, beta)
     if iszero(alpha) || isempty(A) || isempty(B)
diff --git a/test/matmul.jl b/test/matmul.jl
index 1fcf2009..067f49cb 100644
--- a/test/matmul.jl
+++ b/test/matmul.jl
@@ -1241,4 +1241,29 @@ end
     @test C1 ≈ C2
 end
 
+@testset "matmul with zero-less types" begin
+    struct Mod <: Real
+        val::Int
+        modulo::Int
+        Mod(x::Int, y::Int) = new(x % y, y)
+    end
+
+    Base.:+(x::Mod, y::Mod) = Mod(x.val + y.val, x.modulo)
+    Base.:*(x::Mod, y::Mod) = Mod(x.val * y.val, x.modulo)
+    Base.zero(x::Mod) = Mod(0, x.modulo)
+
+    m = Mod.(rand(0:19, 5, 0), 20)
+    @test_throws MethodError m * copy(m')
+    for n in (2, 3, 5)
+        A = rand(0:19, n, n)
+        M = Mod.(A, 20)
+        @test M * M == Mod.(A * A, 20)
+        @test M' * M == Mod.(A' * A, 20)
+        @test M * M' == Mod.(A * A', 20)
+        @test M' * M' == Mod.(A' * A', 20)
+        @test M * M[:, 1] == Mod.(A * A[:, 1], 20)
+        @test M' * M[:, 1] == Mod.(A' * A[:, 1], 20)
+    end
+end
+
 end # module TestMatmul