diff --git a/src/MutableArithmetics.jl b/src/MutableArithmetics.jl
index 3538466..8cc8b0b 100644
--- a/src/MutableArithmetics.jl
+++ b/src/MutableArithmetics.jl
@@ -35,14 +35,11 @@ include("linear_algebra.jl")
 include("sparse_arrays.jl")
 
 isequal_canonical(a, b) = a == b
-function isequal_canonical(a::Array{T, N}, b::Array{T, N}) where {T, N}
+function isequal_canonical(a::AT, b::AT) where AT <: Union{Array, LinearAlgebra.Symmetric}
     return all(zip(a, b)) do elements
         return isequal_canonical(elements...)
     end
 end
-function isequal_canonical(a::LinearAlgebra.Symmetric, b::LinearAlgebra.Symmetric)
-    return isequal_canonical(parent(a), parent(b))
-end
 
 include("rewrite.jl")
 include("dispatch.jl")
diff --git a/src/Test/array.jl b/src/Test/array.jl
index 7784d37..9bb9f39 100644
--- a/src/Test/array.jl
+++ b/src/Test/array.jl
@@ -313,6 +313,14 @@ function symmetric_unary_test(x)
     end
 end
 
+function symmetric_add_test(x)
+    if x isa AbstractMatrix && size(x, 1) == size(x, 2)
+        y = LinearAlgebra.Symmetric(x)
+        add_test(y, y)
+        add_test(x, y)
+    end
+end
+
 function matrix_uniform_scaling_test(x)
     if !(x isa AbstractMatrix && size(x, 1) == size(x, 2))
         return
@@ -347,6 +355,7 @@ const array_tests = Dict(
     "broadcast_division" => broadcast_division_test,
     "unary" => unary_test,
     "symmetric_unary" => symmetric_unary_test,
+    "symmetric_add" => symmetric_add_test,
     "matrix_uniform_scaling" => matrix_uniform_scaling_test,
     "symmetric_matrix_uniform_scaling" => symmetric_matrix_uniform_scaling_test
 )
diff --git a/src/interface.jl b/src/interface.jl
index 65fb131..bed8378 100644
--- a/src/interface.jl
+++ b/src/interface.jl
@@ -10,6 +10,11 @@ Returns the type returned to the call `operate(op, args...)` where the types of
 the arguments `args` are `ArgsTypes`.
 """
 function promote_operation end
+function promote_operation(op::Function, x::Type{<:AbstractArray}, y::Type{<:AbstractArray})
+    # `zero` is not defined for `AbstractArray` so the fallback would fail with a cryptic MethodError.
+    # We replace it by a more helpful error here.
+    error("`promote_operation($op, $x, $y)` not implemented yet, please report this.")
+end
 # Julia v1.0.x has trouble with inference with the `Vararg` method, see
 # https://travis-ci.org/JuliaOpt/JuMP.jl/jobs/617606373
 function promote_operation(op::Function, x::Type, y::Type)
diff --git a/src/linear_algebra.jl b/src/linear_algebra.jl
index 7159e8e..cc8223a 100644
--- a/src/linear_algebra.jl
+++ b/src/linear_algebra.jl
@@ -12,6 +12,9 @@ end
 function promote_operation(op::Union{typeof(+), typeof(-)}, ::Type{Matrix{T}}, ::Type{LinearAlgebra.UniformScaling{S}}) where {S, T}
     return Matrix{promote_operation(op, S, T)}
 end
+function promote_operation(op::Union{typeof(+), typeof(-)}, ::Type{Matrix{T}}, ::Type{<:LinearAlgebra.Symmetric{S}}) where {S, T}
+    return Matrix{promote_operation(op, S, T)}
+end
 
 # Only `Scaling`
 function mutable_operate!(op::Union{typeof(+), typeof(-)}, A::Matrix, B::LinearAlgebra.UniformScaling)
@@ -32,23 +35,35 @@ mul_rhs(::typeof(+)) = add_mul
 mul_rhs(::typeof(-)) = sub_mul
 
 # `Scaling` and `Array`
-function _mutable_operate!(op::Union{typeof(+), typeof(-)}, A::Array{S, N}, B::Array{T, N}, left_factors::Tuple, right_factors::Tuple) where {S, T, N}
+function _mutable_operate!(op::Union{typeof(+), typeof(-)}, A::Array{S, N},
+                           B::Union{Array{T, N}, LinearAlgebra.Symmetric{T}},
+                           left_factors::Tuple, right_factors::Tuple) where {S, T, N}
     for i in eachindex(A)
         A[i] = operate!(mul_rhs(op), A[i], left_factors..., B[i], right_factors...)
     end
     return A
 end
 
+function _check_dims(A, B)
+    if size(A) != size(B)
+        throw(DimensionMismatch("Cannot sum matrices of size `$(size(A))` and size `$(size(B))`, the size of the two matrices must be equal."))
+    end
+end
+
 function mutable_operate!(op::Union{typeof(+), typeof(-)}, A::Array{S, N}, B::AbstractArray{T, N}) where {S, T, N}
+    _check_dims(A, B)
     return _mutable_operate!(op, A, B, tuple(), tuple())
 end
 function mutable_operate!(::typeof(add_mul), A::Array{S, N}, B::AbstractArray{T, N}, α::Vararg{Scaling, M}) where {S, T, N, M}
+    _check_dims(A, B)
     return _mutable_operate!(+, A, B, tuple(), α)
 end
 function mutable_operate!(::typeof(add_mul), A::Array{S, N}, α::Scaling, B::AbstractArray{T, N}, β::Vararg{Scaling, M}) where {S, T, N, M}
+    _check_dims(A, B)
     return _mutable_operate!(+, A, B, (α,), β)
 end
 function mutable_operate!(::typeof(add_mul), A::Array{S, N}, α1::Scaling, α2::Scaling, B::AbstractArray{T, N}, β::Vararg{Scaling, M}) where {S, T, N, M}
+    _check_dims(A, B)
     return _mutable_operate!(+, A, B, (α1, α2), β)
 end
 
@@ -59,6 +74,7 @@ end
 
 # Product
 
+similar_array_type(::Type{LinearAlgebra.Symmetric{T, MT}}, ::Type{S}) where {S, T, MT} = LinearAlgebra.Symmetric{S, similar_array_type(MT, S)}
 similar_array_type(::Type{Array{T, N}}, ::Type{S}) where {S, T, N} = Array{S, N}
 function promote_operation(op::typeof(*), A::Type{<:AbstractArray{T}}, ::Type{S}) where {S, T}
     return similar_array_type(A, promote_operation(op, T, S))
diff --git a/src/shortcuts.jl b/src/shortcuts.jl
index eac3604..ef9237a 100644
--- a/src/shortcuts.jl
+++ b/src/shortcuts.jl
@@ -30,6 +30,9 @@ mul!(args::Vararg{Any, N}) where {N} = operate!(*, args...)
 function promote_operation(::typeof(add_mul), T::Type, x::Type, y::Type)
     return promote_operation(+, T, promote_operation(*, x, y))
 end
+function promote_operation(::typeof(add_mul), x::Type{<:AbstractArray}, y::Type{<:AbstractArray})
+    return promote_operation(+, x, y)
+end
 function promote_operation(::typeof(add_mul), T::Type, args::Vararg{Type, N}) where N
     return promote_operation(+, T, promote_operation(*, args...))
 end
diff --git a/test/matmul.jl b/test/matmul.jl
index febdba0..3467ab2 100644
--- a/test/matmul.jl
+++ b/test/matmul.jl
@@ -4,6 +4,23 @@ const MA = MutableArithmetics
 
 include("utilities.jl")
 
+struct CustomArray{T, N} <: AbstractArray{T, N} end
+
+@testset "Errors" begin
+    @testset "`promote_op` error" begin
+        AT = CustomArray{Int, 3}
+        err = ErrorException("`promote_operation(+, CustomArray{Int64,3}, CustomArray{Int64,3})` not implemented yet, please report this.")
+        @test_throws err MA.promote_operation(+, AT, AT)
+    end
+
+    @testset "Dimension mismatch" begin
+        A = zeros(1, 1)
+        B = zeros(2, 2)
+        err = DimensionMismatch("Cannot sum matrices of size `(1, 1)` and size `(2, 2)`, the size of the two matrices must be equal.")
+        @test_throws err MA.@rewrite A + B
+    end
+end
+
 @testset "Matrix multiplication" begin
     @testset "matrix-vector product" begin
         A = [1 1 1; 1 1 1; 1 1 1]