diff --git a/src/bidiag.jl b/src/bidiag.jl
index 05c1371c..19a80336 100644
--- a/src/bidiag.jl
+++ b/src/bidiag.jl
@@ -613,7 +613,7 @@ function _bibimul!(C, A, B, _add)
     # `_modify!` in the following loop will not update the
     # off-diagonal elements for non-zero beta.
     _rmul_or_fill!(C, _add.beta)
-    iszero(_add.alpha) && return C
+    _iszero_alpha(_add) && return C
     if n <= 3
         # naive multiplication
         for I in CartesianIndices(C)
@@ -858,7 +858,7 @@ function _mul!(C::AbstractMatrix, A::BiTriSym, B::Diagonal, _add::MulAddMul)
     n = size(A,1)
     iszero(n) && return C
     _rmul_or_fill!(C, _add.beta)  # see the same use above
-    iszero(_add.alpha) && return C
+    _iszero_alpha(_add) && return C
     Al = _diag(A, -1)
     Ad = _diag(A, 0)
     Au = _diag(A, 1)
@@ -901,7 +901,7 @@ function _mul!(C::AbstractMatrix, A::Bidiagonal, B::Diagonal, _add::MulAddMul)
     n = size(A,1)
     iszero(n) && return C
     _rmul_or_fill!(C, _add.beta)  # see the same use above
-    iszero(_add.alpha) && return C
+    _iszero_alpha(_add) && return C
     (; dv, ev) = A
     Bd = B.diag
     rowshift = A.uplo == 'U' ? -1 : 1
@@ -930,7 +930,7 @@ function _mul!(C::Bidiagonal, A::Bidiagonal, B::Diagonal, _add::MulAddMul)
     matmul_size_check(size(C), size(A), size(B))
     n = size(A,1)
     iszero(n) && return C
-    iszero(_add.alpha) && return _rmul_or_fill!(C, _add.beta)
+    _iszero_alpha(_add) && return _rmul_or_fill!(C, _add.beta)
     Adv, Aev = A.dv, A.ev
     Cdv, Cev = C.dv, C.ev
     Bd = B.diag
@@ -964,7 +964,7 @@ function _mul!(C::AbstractVecOrMat, A::BiTriSym, B::AbstractVecOrMat, _add::MulA
     nA = size(A,1)
     nB = size(B,2)
     (iszero(nA) || iszero(nB)) && return C
-    iszero(_add.alpha) && return _rmul_or_fill!(C, _add.beta)
+    _iszero_alpha(_add) && return _rmul_or_fill!(C, _add.beta)
     if nA == 1
         A11 = @inbounds A[1,1]
         for i in axes(B, 2)
@@ -1032,7 +1032,7 @@ function _mul!(C::AbstractMatrix, A::AbstractMatrix, B::TriSym, _add::MulAddMul)
     matmul_size_check(size(C), size(A), size(B))
     n = size(A,1)
     m = size(B,2)
-    (iszero(_add.alpha) || iszero(m)) && return _rmul_or_fill!(C, _add.beta)
+    (_iszero_alpha(_add) || iszero(m)) && return _rmul_or_fill!(C, _add.beta)
     if m == 1
         B11 = B[1,1]
         return mul!(C, A, B11, _add.alpha, _add.beta)
@@ -1068,7 +1068,7 @@ function _mul!(C::AbstractMatrix, A::AbstractMatrix, B::Bidiagonal, _add::MulAdd
     matmul_size_check(size(C), size(A), size(B))
     m, n = size(A)
     (iszero(m) || iszero(n)) && return C
-    iszero(_add.alpha) && return _rmul_or_fill!(C, _add.beta)
+    _iszero_alpha(_add) && return _rmul_or_fill!(C, _add.beta)
     @inbounds if B.uplo == 'U'
         for j in n:-1:2, i in 1:m
             _modify!(_add, A[i,j] * B.dv[j] + A[i,j-1] * B.ev[j-1], C, (i, j))
@@ -1100,7 +1100,7 @@ function _dibimul!(C, A, B, _add)
     iszero(n) && return C
     # ensure that we fill off-band elements in the destination
     _rmul_or_fill!(C, _add.beta)
-    iszero(_add.alpha) && return C
+    _iszero_alpha(_add) && return C
     if n <= 3
         # For simplicity, use a naive multiplication for small matrices
         # that loops over all elements.
@@ -1144,7 +1144,7 @@ function _dibimul!(C::AbstractMatrix, A::Diagonal, B::Bidiagonal, _add)
     iszero(n) && return C
     # ensure that we fill off-band elements in the destination
     _rmul_or_fill!(C, _add.beta)
-    iszero(_add.alpha) && return C
+    _iszero_alpha(_add) && return C
     Ad = A.diag
     Bdv, Bev = B.dv, B.ev
     rowshift = B.uplo == 'U' ? -1 : 1
@@ -1173,7 +1173,7 @@ function _dibimul!(C::Bidiagonal, A::Diagonal, B::Bidiagonal, _add)
     matmul_size_check(size(C), size(A), size(B))
     n = size(A,1)
     n == 0 && return C
-    iszero(_add.alpha) && return _rmul_or_fill!(C, _add.beta)
+    _iszero_alpha(_add) && return _rmul_or_fill!(C, _add.beta)
     Ad = A.diag
     Bdv, Bev = B.dv, B.ev
     Cdv, Cev = C.dv, C.ev
diff --git a/src/generic.jl b/src/generic.jl
index de37f081..5b49b8ca 100644
--- a/src/generic.jl
+++ b/src/generic.jl
@@ -124,6 +124,9 @@ MulAddMul() = MulAddMul{true,true,Bool,Bool}(true, false)
 @inline (p::MulAddMul{true, false})(x, y) = x + y * p.beta
 @inline (p::MulAddMul{false, false})(x, y) = x * p.alpha + y * p.beta
 
+_iszero_alpha(m::MulAddMul) = iszero(m.alpha)
+_iszero_alpha(m::MulAddMul{true}) = false
+
 """
     _modify!(_add::MulAddMul, x, C, idx)
 
diff --git a/src/triangular.jl b/src/triangular.jl
index ad66f492..ff8d19da 100644
--- a/src/triangular.jl
+++ b/src/triangular.jl
@@ -692,7 +692,7 @@ end
 
 function _triscale!(A::UpperTriangular, B::UpperTriangular, c::Number, _add)
     checksize1(A, B)
-    iszero(_add.alpha) && return _rmul_or_fill!(A, _add.beta)
+    _iszero_alpha(_add) && return _rmul_or_fill!(A, _add.beta)
     for j in axes(B.data,2)
         for i in firstindex(B.data,1):j
             @inbounds _modify!(_add, B.data[i,j] * c, A.data, (i,j))
@@ -702,7 +702,7 @@ function _triscale!(A::UpperTriangular, B::UpperTriangular, c::Number, _add)
 end
 function _triscale!(A::UpperTriangular, c::Number, B::UpperTriangular, _add)
     checksize1(A, B)
-    iszero(_add.alpha) && return _rmul_or_fill!(A, _add.beta)
+    _iszero_alpha(_add) && return _rmul_or_fill!(A, _add.beta)
     for j in axes(B.data,2)
         for i in firstindex(B.data,1):j
             @inbounds _modify!(_add, c * B.data[i,j], A.data, (i,j))
@@ -712,7 +712,7 @@ function _triscale!(A::UpperTriangular, c::Number, B::UpperTriangular, _add)
 end
 function _triscale!(A::UpperOrUnitUpperTriangular, B::UnitUpperTriangular, c::Number, _add)
     checksize1(A, B)
-    iszero(_add.alpha) && return _rmul_or_fill!(A, _add.beta)
+    _iszero_alpha(_add) && return _rmul_or_fill!(A, _add.beta)
     for j in axes(B.data,2)
         @inbounds _modify!(_add, c, A, (j,j))
         for i in firstindex(B.data,1):(j - 1)
@@ -723,7 +723,7 @@ function _triscale!(A::UpperOrUnitUpperTriangular, B::UnitUpperTriangular, c::Nu
 end
 function _triscale!(A::UpperOrUnitUpperTriangular, c::Number, B::UnitUpperTriangular, _add)
     checksize1(A, B)
-    iszero(_add.alpha) && return _rmul_or_fill!(A, _add.beta)
+    _iszero_alpha(_add) && return _rmul_or_fill!(A, _add.beta)
     for j in axes(B.data,2)
         @inbounds _modify!(_add, c, A, (j,j))
         for i in firstindex(B.data,1):(j - 1)
@@ -734,7 +734,7 @@ function _triscale!(A::UpperOrUnitUpperTriangular, c::Number, B::UnitUpperTriang
 end
 function _triscale!(A::LowerTriangular, B::LowerTriangular, c::Number, _add)
     checksize1(A, B)
-    iszero(_add.alpha) && return _rmul_or_fill!(A, _add.beta)
+    _iszero_alpha(_add) && return _rmul_or_fill!(A, _add.beta)
     for j in axes(B.data,2)
         for i in j:lastindex(B.data,1)
             @inbounds _modify!(_add, B.data[i,j] * c, A.data, (i,j))
@@ -744,7 +744,7 @@ function _triscale!(A::LowerTriangular, B::LowerTriangular, c::Number, _add)
 end
 function _triscale!(A::LowerTriangular, c::Number, B::LowerTriangular, _add)
     checksize1(A, B)
-    iszero(_add.alpha) && return _rmul_or_fill!(A, _add.beta)
+    _iszero_alpha(_add) && return _rmul_or_fill!(A, _add.beta)
     for j in axes(B.data,2)
         for i in j:lastindex(B.data,1)
             @inbounds _modify!(_add, c * B.data[i,j], A.data, (i,j))
@@ -754,7 +754,7 @@ function _triscale!(A::LowerTriangular, c::Number, B::LowerTriangular, _add)
 end
 function _triscale!(A::LowerOrUnitLowerTriangular, B::UnitLowerTriangular, c::Number, _add)
     checksize1(A, B)
-    iszero(_add.alpha) && return _rmul_or_fill!(A, _add.beta)
+    _iszero_alpha(_add) && return _rmul_or_fill!(A, _add.beta)
     for j in axes(B.data,2)
         @inbounds _modify!(_add, c, A, (j,j))
         for i in (j + 1):lastindex(B.data,1)
@@ -765,7 +765,7 @@ function _triscale!(A::LowerOrUnitLowerTriangular, B::UnitLowerTriangular, c::Nu
 end
 function _triscale!(A::LowerOrUnitLowerTriangular, c::Number, B::UnitLowerTriangular, _add)
     checksize1(A, B)
-    iszero(_add.alpha) && return _rmul_or_fill!(A, _add.beta)
+    _iszero_alpha(_add) && return _rmul_or_fill!(A, _add.beta)
     for j in axes(B.data,2)
         @inbounds _modify!(_add, c, A, (j,j))
         for i in (j + 1):lastindex(B.data,1)
diff --git a/test/bidiag.jl b/test/bidiag.jl
index e111433d..2488cd3f 100644
--- a/test/bidiag.jl
+++ b/test/bidiag.jl
@@ -996,7 +996,9 @@ end
             @test A * D ≈ mul!(S, A, D) ≈ M * D
             @test D * A ≈ mul!(S, D, A) ≈ D * M
             @test mul!(copy(S), D, A, 2, 2) ≈ D * M * 2 + S * 2
+            @test mul!(copy(S), D, A, 0, 2) ≈ D * M * 0 + S * 2
             @test mul!(copy(S), A, D, 2, 2) ≈ M * D * 2 + S * 2
+            @test mul!(copy(S), A, D, 0, 2) ≈ M * D * 0 + S * 2
 
             A2 = Bidiagonal(dv, zero(ev), uplo)
             M2 = Array(A2)
@@ -1074,10 +1076,12 @@ end
             @test B * v ≈ M * v
             @test mul!(similar(v), B, v) ≈ M * v
             @test mul!(ones(size(v)), B, v, 2, 3) ≈ M * v * 2 .+ 3
+            @test mul!(ones(size(v)), B, v, 0, 3) ≈ M * v * 0 .+ 3
 
             @test B * B ≈ M * M
             @test mul!(similar(B, size(B)), B, B) ≈ M * M
             @test mul!(ones(size(B)), B, B, 2, 4) ≈ M * M * 2 .+ 4
+            @test mul!(ones(size(B)), B, B, 0, 4) ≈ M * M * 0 .+ 4
 
             for m in 0:6
                 AL = rand(m,n)