diff --git a/stdlib/SparseArrays/src/deprecated.jl b/stdlib/SparseArrays/src/deprecated.jl
index 76f9f461a9b1e..803268f141444 100644
--- a/stdlib/SparseArrays/src/deprecated.jl
+++ b/stdlib/SparseArrays/src/deprecated.jl
@@ -159,13 +159,13 @@ using LinearAlgebra: Adjoint, Transpose
 @deprecate A_mul_B!(C::StridedVecOrMat, A::SparseMatrixCSC, B::StridedVecOrMat)     mul!(C, A, B)
 @deprecate Ac_mul_B!(C::StridedVecOrMat, A::SparseMatrixCSC, B::StridedVecOrMat)    mul!(C, adjoint(A), B)
 @deprecate At_mul_B!(C::StridedVecOrMat, A::SparseMatrixCSC, B::StridedVecOrMat)    mul!(C, transpose(A), B)
-@deprecate A_mul_B!(α::Number, A::SparseMatrixCSC, B::StridedVecOrMat, β::Number, C::StridedVecOrMat)   mul!(α, A, B, β, C)
+@deprecate A_mul_B!(α::Number, A::SparseMatrixCSC, B::StridedVecOrMat, β::Number, C::StridedVecOrMat)   mul!(C, A, B, α, β)
 @deprecate A_mul_B(A::SparseMatrixCSC{TA,S}, x::StridedVector{Tx}) where {TA,S,Tx}  (*)(A, x)
 @deprecate A_mul_B(A::SparseMatrixCSC{TA,S}, B::StridedMatrix{Tx}) where {TA,S,Tx}  (*)(A, B)
-@deprecate Ac_mul_B!(α::Number, A::SparseMatrixCSC, B::StridedVecOrMat, β::Number, C::StridedVecOrMat)  mul!(α, adjoint(A), B, β, C)
+@deprecate Ac_mul_B!(α::Number, A::SparseMatrixCSC, B::StridedVecOrMat, β::Number, C::StridedVecOrMat)  mul!(C, adjoint(A), B, α, β)
 @deprecate Ac_mul_B(A::SparseMatrixCSC{TA,S}, x::StridedVector{Tx}) where {TA,S,Tx}     (*)(adjoint(A), x)
 @deprecate Ac_mul_B(A::SparseMatrixCSC{TA,S}, B::StridedMatrix{Tx}) where {TA,S,Tx}     (*)(adjoint(A), B)
-@deprecate At_mul_B!(α::Number, A::SparseMatrixCSC, B::StridedVecOrMat, β::Number, C::StridedVecOrMat)  mul!(α, transpose(A), B, β, C)
+@deprecate At_mul_B!(α::Number, A::SparseMatrixCSC, B::StridedVecOrMat, β::Number, C::StridedVecOrMat)  mul!(C, transpose(A), B, α, β)
 @deprecate At_mul_B(A::SparseMatrixCSC{TA,S}, x::StridedVector{Tx}) where {TA,S,Tx}     (*)(transpose(A), x)
 @deprecate At_mul_B(A::SparseMatrixCSC{TA,S}, B::StridedMatrix{Tx}) where {TA,S,Tx}     (*)(transpose(A), B)
 @deprecate A_mul_Bt(A::SparseMatrixCSC{TvA,TiA}, B::SparseMatrixCSC{TvB,TiB}) where {TvA,TiA,TvB,TiB}   (*)(A, transpose(B))
@@ -197,16 +197,16 @@ end
 using LinearAlgebra: Adjoint, Transpose
 @deprecate Ac_mul_B(A::SparseMatrixCSC, x::AbstractSparseVector)    (*)(adjoint(A), x)
 @deprecate At_mul_B(A::SparseMatrixCSC, x::AbstractSparseVector)    (*)(transpose(A), x)
-@deprecate Ac_mul_B!(α::Number, A::SparseMatrixCSC, x::AbstractSparseVector, β::Number, y::StridedVector)   mul!(α, adjoint(A), x, β, y)
+@deprecate Ac_mul_B!(α::Number, A::SparseMatrixCSC, x::AbstractSparseVector, β::Number, y::StridedVector)   mul!(y, adjoint(A), x, α, β)
 @deprecate Ac_mul_B!(y::StridedVector{Ty}, A::SparseMatrixCSC, x::AbstractSparseVector{Tx}) where {Tx,Ty}   mul!(y, adjoint(A), x)
-@deprecate At_mul_B!(α::Number, A::SparseMatrixCSC, x::AbstractSparseVector, β::Number, y::StridedVector)   mul!(α, transpose(A), x, β, y)
+@deprecate At_mul_B!(α::Number, A::SparseMatrixCSC, x::AbstractSparseVector, β::Number, y::StridedVector)   mul!(y, transpose(A), x, α, β)
 @deprecate At_mul_B!(y::StridedVector{Ty}, A::SparseMatrixCSC, x::AbstractSparseVector{Tx}) where {Tx,Ty}   mul!(y, transpose(A), x)
-@deprecate A_mul_B!(α::Number, A::SparseMatrixCSC, x::AbstractSparseVector, β::Number, y::StridedVector)    mul!(α, A, x, β, y)
+@deprecate A_mul_B!(α::Number, A::SparseMatrixCSC, x::AbstractSparseVector, β::Number, y::StridedVector)    mul!(y, A, x, α, β)
 @deprecate A_mul_B!(y::StridedVector{Ty}, A::SparseMatrixCSC, x::AbstractSparseVector{Tx}) where {Tx,Ty}    mul!(y, A, x)
-@deprecate At_mul_B!(α::Number, A::StridedMatrix, x::AbstractSparseVector, β::Number, y::StridedVector)     mul!(α, transpose(A), x, β, y)
+@deprecate At_mul_B!(α::Number, A::StridedMatrix, x::AbstractSparseVector, β::Number, y::StridedVector)     mul!(y, transpose(A), x, α, β)
 @deprecate At_mul_B!(y::StridedVector{Ty}, A::StridedMatrix, x::AbstractSparseVector{Tx}) where {Tx,Ty}     mul!(y, transpose(A), x)
 @deprecate At_mul_B(A::StridedMatrix{Ta}, x::AbstractSparseVector{Tx}) where {Ta,Tx}    (*)(transpose(A), x)
-@deprecate A_mul_B!(α::Number, A::StridedMatrix, x::AbstractSparseVector, β::Number, y::StridedVector)  mul!(α, A, x, β, y)
+@deprecate A_mul_B!(α::Number, A::StridedMatrix, x::AbstractSparseVector, β::Number, y::StridedVector)  mul!(y, A, x, α, β)
 @deprecate A_mul_B!(y::StridedVector{Ty}, A::StridedMatrix, x::AbstractSparseVector{Tx}) where {Tx,Ty}  mul!(y, A, x)
 
 # methods involving RowVector from base/sparse/linalg.jl, to deprecate
diff --git a/stdlib/SparseArrays/src/linalg.jl b/stdlib/SparseArrays/src/linalg.jl
index d9aa4238df152..250837b0c4d61 100644
--- a/stdlib/SparseArrays/src/linalg.jl
+++ b/stdlib/SparseArrays/src/linalg.jl
@@ -29,7 +29,7 @@ end
 
 # In matrix-vector multiplication, the correct orientation of the vector is assumed.
 
-function mul!(α::Number, A::SparseMatrixCSC, B::StridedVecOrMat, β::Number, C::StridedVecOrMat)
+function mul!(C::StridedVecOrMat, A::SparseMatrixCSC, B::StridedVecOrMat, α::Number, β::Number)
     A.n == size(B, 1) || throw(DimensionMismatch())
     A.m == size(C, 1) || throw(DimensionMismatch())
     size(B, 2) == size(C, 2) || throw(DimensionMismatch())
@@ -49,11 +49,11 @@ function mul!(α::Number, A::SparseMatrixCSC, B::StridedVecOrMat, β::Number, C:
     C
 end
 *(A::SparseMatrixCSC{TA,S}, x::StridedVector{Tx}) where {TA,S,Tx} =
-    (T = promote_type(TA, Tx); mul!(one(T), A, x, zero(T), similar(x, T, A.m)))
+    (T = promote_type(TA, Tx); mul!(similar(x, T, A.m), A, x, one(T), zero(T)))
 *(A::SparseMatrixCSC{TA,S}, B::StridedMatrix{Tx}) where {TA,S,Tx} =
-    (T = promote_type(TA, Tx); mul!(one(T), A, B, zero(T), similar(B, T, (A.m, size(B, 2)))))
+    (T = promote_type(TA, Tx); mul!(similar(B, T, (A.m, size(B, 2))), A, B, one(T), zero(T)))
 
-function mul!(α::Number, adjA::Adjoint{<:Any,<:SparseMatrixCSC}, B::StridedVecOrMat, β::Number, C::StridedVecOrMat)
+function mul!(C::StridedVecOrMat, adjA::Adjoint{<:Any,<:SparseMatrixCSC}, B::StridedVecOrMat, α::Number, β::Number)
     A = adjA.parent
     A.n == size(C, 1) || throw(DimensionMismatch())
     A.m == size(B, 1) || throw(DimensionMismatch())
@@ -75,11 +75,11 @@ function mul!(α::Number, adjA::Adjoint{<:Any,<:SparseMatrixCSC}, B::StridedVecO
     C
 end
 *(adjA::Adjoint{<:Any,<:SparseMatrixCSC{TA,S}}, x::StridedVector{Tx}) where {TA,S,Tx} =
-    (A = adjA.parent; T = promote_type(TA, Tx); mul!(one(T), adjoint(A), x, zero(T), similar(x, T, A.n)))
+    (A = adjA.parent; T = promote_type(TA, Tx); mul!(similar(x, T, A.n), adjoint(A), x, one(T), zero(T)))
 *(adjA::Adjoint{<:Any,<:SparseMatrixCSC{TA,S}}, B::StridedMatrix{Tx}) where {TA,S,Tx} =
-    (A = adjA.parent; T = promote_type(TA, Tx); mul!(one(T), adjoint(A), B, zero(T), similar(B, T, (A.n, size(B, 2)))))
+    (A = adjA.parent; T = promote_type(TA, Tx); mul!(similar(B, T, (A.n, size(B, 2))), adjoint(A), B, one(T), zero(T)))
 
-function mul!(α::Number, transA::Transpose{<:Any,<:SparseMatrixCSC}, B::StridedVecOrMat, β::Number, C::StridedVecOrMat)
+function mul!(C::StridedVecOrMat, transA::Transpose{<:Any,<:SparseMatrixCSC}, B::StridedVecOrMat, α::Number, β::Number)
     A = transA.parent
     A.n == size(C, 1) || throw(DimensionMismatch())
     A.m == size(B, 1) || throw(DimensionMismatch())
@@ -101,18 +101,18 @@ function mul!(α::Number, transA::Transpose{<:Any,<:SparseMatrixCSC}, B::Strided
     C
 end
 *(transA::Transpose{<:Any,<:SparseMatrixCSC{TA,S}}, x::StridedVector{Tx}) where {TA,S,Tx} =
-    (A = transA.parent; T = promote_type(TA, Tx); mul!(one(T), transpose(A), x, zero(T), similar(x, T, A.n)))
+    (A = transA.parent; T = promote_type(TA, Tx); mul!(similar(x, T, A.n), transpose(A), x, one(T), zero(T)))
 *(transA::Transpose{<:Any,<:SparseMatrixCSC{TA,S}}, B::StridedMatrix{Tx}) where {TA,S,Tx} =
-    (A = transA.parent; T = promote_type(TA, Tx); mul!(one(T), transpose(A), B, zero(T), similar(B, T, (A.n, size(B, 2)))))
+    (A = transA.parent; T = promote_type(TA, Tx); mul!(similar(B, T, (A.n, size(B, 2))), transpose(A), B, one(T), zero(T)))
 
 # For compatibility with dense multiplication API. Should be deleted when dense multiplication
 # API is updated to follow BLAS API.
 mul!(C::StridedVecOrMat, A::SparseMatrixCSC, B::StridedVecOrMat) =
-    mul!(one(eltype(B)), A, B, zero(eltype(C)), C)
+    mul!(C, A, B, one(eltype(B)), zero(eltype(C)))
 mul!(C::StridedVecOrMat, adjA::Adjoint{<:Any,<:SparseMatrixCSC}, B::StridedVecOrMat) =
-    (A = adjA.parent; mul!(one(eltype(B)), adjoint(A), B, zero(eltype(C)), C))
+    (A = adjA.parent; mul!(C, adjoint(A), B, one(eltype(B)), zero(eltype(C))))
 mul!(C::StridedVecOrMat, transA::Transpose{<:Any,<:SparseMatrixCSC}, B::StridedVecOrMat) =
-    (A = transA.parent; mul!(one(eltype(B)), transpose(A), B, zero(eltype(C)), C))
+    (A = transA.parent; mul!(C, transpose(A), B, one(eltype(B)), zero(eltype(C))))
 
 function (*)(X::StridedMatrix{TX}, A::SparseMatrixCSC{TvA,TiA}) where {TX,TvA,TiA}
     mX, nX = size(X)
diff --git a/stdlib/SparseArrays/src/sparsevector.jl b/stdlib/SparseArrays/src/sparsevector.jl
index fae9d203cb770..e4d89ab7e442a 100644
--- a/stdlib/SparseArrays/src/sparsevector.jl
+++ b/stdlib/SparseArrays/src/sparsevector.jl
@@ -1581,9 +1581,9 @@ function (*)(A::StridedMatrix{Ta}, x::AbstractSparseVector{Tx}) where {Ta,Tx}
 end
 
 mul!(y::AbstractVector{Ty}, A::StridedMatrix, x::AbstractSparseVector{Tx}) where {Tx,Ty} =
-    mul!(one(Tx), A, x, zero(Ty), y)
+    mul!(y, A, x, one(Tx), zero(Ty))
 
-function mul!(α::Number, A::StridedMatrix, x::AbstractSparseVector, β::Number, y::AbstractVector)
+function mul!(y::AbstractVector, A::StridedMatrix, x::AbstractSparseVector, α::Number, β::Number)
     m, n = size(A)
     length(x) == n && length(y) == m || throw(DimensionMismatch())
     m == 0 && return y
@@ -1619,9 +1619,9 @@ function *(transA::Transpose{<:Any,<:StridedMatrix{Ta}}, x::AbstractSparseVector
 end
 
 mul!(y::AbstractVector{Ty}, transA::Transpose{<:Any,<:StridedMatrix}, x::AbstractSparseVector{Tx}) where {Tx,Ty} =
-    (A = transA.parent; mul!(one(Tx), transpose(A), x, zero(Ty), y))
+    (A = transA.parent; mul!(y, transpose(A), x, one(Tx), zero(Ty)))
 
-function mul!(α::Number, transA::Transpose{<:Any,<:StridedMatrix}, x::AbstractSparseVector, β::Number, y::AbstractVector)
+function mul!(y::AbstractVector, transA::Transpose{<:Any,<:StridedMatrix}, x::AbstractSparseVector, α::Number, β::Number)
     A = transA.parent
     m, n = size(A)
     length(x) == m && length(y) == n || throw(DimensionMismatch())
@@ -1678,9 +1678,9 @@ end
 # * and mul!
 
 mul!(y::AbstractVector{Ty}, A::SparseMatrixCSC, x::AbstractSparseVector{Tx}) where {Tx,Ty} =
-    mul!(one(Tx), A, x, zero(Ty), y)
+    mul!(y, A, x, one(Tx), zero(Ty))
 
-function mul!(α::Number, A::SparseMatrixCSC, x::AbstractSparseVector, β::Number, y::AbstractVector)
+function mul!(y::AbstractVector, A::SparseMatrixCSC, x::AbstractSparseVector, α::Number, β::Number)
     m, n = size(A)
     length(x) == n && length(y) == m || throw(DimensionMismatch())
     m == 0 && return y
@@ -1711,20 +1711,20 @@ end
 # * and *(Tranpose(A), B)
 
 mul!(y::AbstractVector{Ty}, transA::Transpose{<:Any,<:SparseMatrixCSC}, x::AbstractSparseVector{Tx}) where {Tx,Ty} =
-    (A = transA.parent; mul!(one(Tx), transpose(A), x, zero(Ty), y))
+    (A = transA.parent; mul!(y, transpose(A), x, one(Tx), zero(Ty)))
 
-mul!(α::Number, transA::Transpose{<:Any,<:SparseMatrixCSC}, x::AbstractSparseVector, β::Number, y::AbstractVector) =
-    (A = transA.parent; _At_or_Ac_mul_B!(*, α, A, x, β, y))
+mul!(y::AbstractVector, transA::Transpose{<:Any,<:SparseMatrixCSC}, x::AbstractSparseVector, α::Number, β::Number) =
+    (A = transA.parent; _At_or_Ac_mul_B!(*, y, A, x, α, β))
 
 mul!(y::AbstractVector{Ty}, adjA::Adjoint{<:Any,<:SparseMatrixCSC}, x::AbstractSparseVector{Tx}) where {Tx,Ty} =
-    (A = adjA.parent; mul!(one(Tx), adjoint(A), x, zero(Ty), y))
+    (A = adjA.parent; mul!(y, adjoint(A), x, one(Tx), zero(Ty)))
 
-mul!(α::Number, adjA::Adjoint{<:Any,<:SparseMatrixCSC}, x::AbstractSparseVector, β::Number, y::AbstractVector) =
-    (A = adjA.parent; _At_or_Ac_mul_B!(dot, α, A, x, β, y))
+mul!(y::AbstractVector, adjA::Adjoint{<:Any,<:SparseMatrixCSC}, x::AbstractSparseVector, α::Number, β::Number) =
+    (A = adjA.parent; _At_or_Ac_mul_B!(dot, y, A, x, α, β))
 
 function _At_or_Ac_mul_B!(tfun::Function,
-                          α::Number, A::SparseMatrixCSC, x::AbstractSparseVector,
-                          β::Number, y::AbstractVector)
+                          y::AbstractVector, A::SparseMatrixCSC, x::AbstractSparseVector,
+                          α::Number, β::Number)
     m, n = size(A)
     length(x) == m && length(y) == n || throw(DimensionMismatch())
     n == 0 && return y
diff --git a/stdlib/SparseArrays/test/sparsevector.jl b/stdlib/SparseArrays/test/sparsevector.jl
index 0604470cf4ee8..268263191cb78 100644
--- a/stdlib/SparseArrays/test/sparsevector.jl
+++ b/stdlib/SparseArrays/test/sparsevector.jl
@@ -822,7 +822,7 @@ end
             for α in [0.0, 1.0, 2.0], β in [0.0, 0.5, 1.0]
                 y = rand(9)
                 rr = α*A*xf + β*y
-                @test mul!(α, A, x, β, y) === y
+                @test mul!(y, A, x, α, β) === y
                 @test y ≈ rr
             end
             y = A*x
@@ -835,7 +835,7 @@ end
             for α in [0.0, 1.0, 2.0], β in [0.0, 0.5, 1.0]
                 y = rand(9)
                 rr = α*A'xf + β*y
-                @test mul!(α, transpose(A), x, β, y) === y
+                @test mul!(y, transpose(A), x, α, β) === y
                 @test y ≈ rr
             end
             y = *(transpose(A), x)
@@ -850,7 +850,7 @@ end
             for α in [0.0, 1.0, 2.0], β in [0.0, 0.5, 1.0]
                 y = rand(9)
                 rr = α*Af*xf + β*y
-                @test mul!(α, A, x, β, y) === y
+                @test mul!(y, A, x, α, β) === y
                 @test y ≈ rr
             end
             y = SparseArrays.densemv(A, x)
@@ -864,7 +864,7 @@ end
             for α in [0.0, 1.0, 2.0], β in [0.0, 0.5, 1.0]
                 y = rand(9)
                 rr = α*Af'xf + β*y
-                @test mul!(α, transpose(A), x, β, y) === y
+                @test mul!(y, transpose(A), x, α, β) === y
                 @test y ≈ rr
             end
             y = SparseArrays.densemv(A, x; trans='T')
@@ -1269,4 +1269,4 @@ end
     end
 end
 
-end # module
\ No newline at end of file
+end # module