diff --git a/src/identity.jl b/src/identity.jl
index 72e4b0b2..b23ab7e0 100644
--- a/src/identity.jl
+++ b/src/identity.jl
@@ -98,6 +98,8 @@ function Base.setindex!(𝐼::IdentityMultiple, X, inds...)
 end
 
 Base.:(-)(𝐼::IdentityMultiple) = IdentityMultiple(-𝐼.M, 𝐼.n)
+Base.:(+)(𝐼::IdentityMultiple, M::AbstractMatrix) = 𝐼.M + M
+Base.:(+)(M::AbstractMatrix, 𝐼::IdentityMultiple) = M + 𝐼.M
 Base.:(*)(x::Number, 𝐼::IdentityMultiple) = IdentityMultiple(x * 𝐼.M, 𝐼.n)
 Base.:(*)(𝐼::IdentityMultiple, x::Number) = IdentityMultiple(x * 𝐼.M, 𝐼.n)
 Base.:(/)(𝐼::IdentityMultiple, x::Number) = IdentityMultiple(𝐼.M / x, 𝐼.n)
@@ -166,3 +168,7 @@ LinearAlgebra.I(n::Int, N::DataType=Float64) = IdentityMultiple(one(N)*I, n)
 # callable identity matrix given the scaling factor and the size
 IdentityMultiple(λ::Number, n::Int) = IdentityMultiple(λ*I, n)
 LinearAlgebra.I(λ::Number, n::Int) = IdentityMultiple(λ*I, n)
+
+function LinearAlgebra.Hermitian(𝐼::IdentityMultiple)
+    return Hermitian(Diagonal(fill(𝐼.M.λ, 𝐼.n)))
+end
diff --git a/test/identity.jl b/test/identity.jl
index 221fdb7b..b716f89d 100644
--- a/test/identity.jl
+++ b/test/identity.jl
@@ -51,4 +51,11 @@ end
 
     @test I(2) / I == IdentityMultiple(1.0, 2)
     @test I(2) - I(2) == 0.0I(2)
+
+    @test I(2) + [3 3; 1 2] == [4 3; 1 3.]
+    @test [3 3; 1 2] + I(2) == [4 3; 1 3.]
+end
+
+@testset "Specific methods for IdentityMultiple" begin
+    @test Hermitian(I(2)) == Hermitian([1. 0; 0 1])
 end