diff --git a/src/matrix_groups/Spn.jl b/src/matrix_groups/Spn.jl
index 2361050..7bcfbce 100644
--- a/src/matrix_groups/Spn.jl
+++ b/src/matrix_groups/Spn.jl
@@ -24,15 +24,21 @@ Base.show(io::IO, ::SymplecticGroup{N,T}) where {N,T} = print(io, "Sp{$N,$T}")
 function Base.show(io::IO, ::MIME"text/plain", ::SymplecticGroup{N}) where {N}
     return print(io, "group of $N×$N symplectic matrices")
 end
-_offdiag_idcs(n) = ((i, j) for i in 1:n for j in 1:n if i ≠ j)
 
-function symplectic_gens(N, T=Int8)
+function symplectic_gens(N, T = Int8)
     iseven(N) || throw(ArgumentError("N needs to be even!"))
     n = N ÷ 2
 
-    a_ijs = [ElementarySymplectic{N}(:A, i, j, one(T)) for (i, j) in _offdiag_idcs(n)]
+    _offdiag_idcs(n) = ((i, j) for i in 1:n for j in 1:n if i ≠ j)
+
+    a_ijs = [
+        ElementarySymplectic{N}(:A, i, j, one(T)) for (i, j) in _offdiag_idcs(n)
+    ]
     b_is = [ElementarySymplectic{N}(:B, n + i, i, one(T)) for i in 1:n]
-    c_ijs = [ElementarySymplectic{N}(:B, n + i, j, one(T)) for (i, j) in _offdiag_idcs(n)]
+    c_ijs = [
+        ElementarySymplectic{N}(:B, n + i, j, one(T)) for
+        (i, j) in _offdiag_idcs(n)
+    ]
 
     S = [a_ijs; b_is; c_ijs]
 
@@ -49,11 +55,16 @@ function _std_symplectic_form(m::AbstractMatrix)
     n = r ÷ 2
     𝕆 = zeros(eltype(m), n, n)
     𝕀 = one(eltype(m)) * LinearAlgebra.I
-    Ω = [𝕆 -𝕀
-        𝕀 𝕆]
+    Ω = [
+        𝕆 -𝕀
+        𝕀 𝕆
+    ]
     return Ω
 end
 
-function issymplectic(mat::M, Ω=_std_symplectic_form(mat)) where {M<:AbstractMatrix}
+function issymplectic(
+    mat::M,
+    Ω = _std_symplectic_form(mat),
+) where {M<:AbstractMatrix}
     return Ω == transpose(mat) * Ω * mat
 end
diff --git a/src/matrix_groups/abstract.jl b/src/matrix_groups/abstract.jl
index 3caca2c..ac2b625 100644
--- a/src/matrix_groups/abstract.jl
+++ b/src/matrix_groups/abstract.jl
@@ -1,26 +1,31 @@
 abstract type AbstractMatrixGroup{N,T} <: Groups.AbstractFPGroup end
-const MatrixGroupElement{N,T} = Groups.AbstractFPGroupElement{<:AbstractMatrixGroup{N,T}}
+const MatrixGroupElement{N,T} =
+    Groups.AbstractFPGroupElement{<:AbstractMatrixGroup{N,T}}
 
-Base.isone(g::MatrixGroupElement{N,T}) where {N,T} =
-    isone(word(g)) || isone(matrix(g))
+function Base.isone(g::MatrixGroupElement{N,T}) where {N,T}
+    return isone(word(g)) || isone(matrix(g))
+end
 
-function Base.:(==)(m1::M1, m2::M2) where {M1<:MatrixGroupElement,M2<:MatrixGroupElement}
+function Base.:(==)(
+    m1::M1,
+    m2::M2,
+) where {M1<:MatrixGroupElement,M2<:MatrixGroupElement}
     parent(m1) === parent(m2) || return false
     word(m1) == word(m2) && return true
     return matrix(m1) == matrix(m2)
 end
 
-Base.size(m::MatrixGroupElement{N}) where {N} = (N, N)
-Base.eltype(m::MatrixGroupElement{N,T}) where {N,T} = T
+Base.size(::MatrixGroupElement{N}) where {N} = (N, N)
+Base.size(::MatrixGroupElement{N}, d) where {N} = ifelse(d::Integer <= 2, N, 1)
+Base.eltype(::MatrixGroupElement{N,T}) where {N,T} = T
 
 # three structural assumptions about matrix groups
-Groups.word(sl::MatrixGroupElement) = sl.word
-Base.parent(sl::MatrixGroupElement) = sl.parent
-Groups.alphabet(M::MatrixGroup) = M.alphabet
-Groups.rewriting(M::MatrixGroup) = alphabet(M)
+Groups.word(m::MatrixGroupElement) = m.word
+Base.parent(m::MatrixGroupElement) = m.parent
+Groups.alphabet(M::AbstractMatrixGroup) = M.alphabet
+Groups.rewriting(M::AbstractMatrixGroup) = alphabet(M)
 
-Base.hash(m::MatrixGroupElement, h::UInt) =
-    hash(matrix(m), hash(parent(m), h))
+Base.hash(m::MatrixGroupElement, h::UInt) = hash(matrix(m), hash(parent(m), h))
 
 function matrix(m::MatrixGroupElement{N,T}) where {N,T}
     if isone(word(m))
@@ -30,37 +35,55 @@ function matrix(m::MatrixGroupElement{N,T}) where {N,T}
     return prod(matrix(A[l]) for l in word(m))
 end
 
+function Base.convert(
+    ::Type{M},
+    m::MatrixGroupElement,
+) where {M<:AbstractMatrix}
+    return convert(M, matrix(m))
+end
+(M::Type{<:AbstractMatrix})(m::MatrixGroupElement) = convert(M, m)
+
 function Base.rand(
     rng::Random.AbstractRNG,
     rs::Random.SamplerTrivial{<:AbstractMatrixGroup},
 )
     Mgroup = rs[]
     S = gens(Mgroup)
-    return prod(g -> rand(rng, Bool) ? g : inv(g), rand(rng, S, rand(rng, 1:30)))
+    return prod(
+        g -> rand(rng, Bool) ? g : inv(g),
+        rand(rng, S, rand(rng, 1:30)),
+    )
 end
 
 function Base.show(io::IO, M::AbstractMatrixGroup)
     g = gens(M, 1)
     N = size(g, 1)
-    print(io, "H ⩽ GL{$N,$(eltype(g))}")
+    return print(io, "H ⩽ GL{$N,$(eltype(g))}")
 end
 
 function Base.show(io::IO, ::MIME"text/plain", M::AbstractMatrixGroup)
     N = size(gens(M, 1), 1)
     ng = GroupsCore.ngens(M)
-    print(io, "subgroup of $N×$N invertible matrices with $(ng) generators")
+    return print(
+        io,
+        "subgroup of $N×$N invertible matrices with $(ng) generators",
+    )
 end
 
-Base.show(io::IO, mat::Groups.AbstractFPGroupElement{<:AbstractMatrixGroup}) =
-    KnuthBendix.print_repr(io, word(mat), alphabet(mat))
+function Base.show(
+    io::IO,
+    mat::Groups.AbstractFPGroupElement{<:AbstractMatrixGroup},
+)
+    return KnuthBendix.print_repr(io, word(mat), alphabet(mat))
+end
 
 function Base.show(
     io::IO,
     ::MIME"text/plain",
-    mat::Groups.AbstractFPGroupElement{<:AbstractMatrixGroup{N}}
+    mat::Groups.AbstractFPGroupElement{<:AbstractMatrixGroup{N}},
 ) where {N}
     Groups.normalform!(mat)
     KnuthBendix.print_repr(io, word(mat), alphabet(mat))
     println(io, " ∈ ", parent(mat))
-    Base.print_array(io, matrix(mat))
+    return Base.print_array(io, matrix(mat))
 end
diff --git a/src/matrix_groups/eltary_matrices.jl b/src/matrix_groups/eltary_matrices.jl
index 42b582d..8181b11 100644
--- a/src/matrix_groups/eltary_matrices.jl
+++ b/src/matrix_groups/eltary_matrices.jl
@@ -2,23 +2,27 @@ struct ElementaryMatrix{N,T} <: Groups.GSymbol
     i::Int
     j::Int
     val::T
-    ElementaryMatrix{N}(i, j, val=1) where {N} =
-        (@assert i ≠ j; new{N,typeof(val)}(i, j, val))
+    function ElementaryMatrix{N}(i, j, val = 1) where {N}
+        return (@assert i ≠ j; new{N,typeof(val)}(i, j, val))
+    end
 end
 
 function Base.show(io::IO, e::ElementaryMatrix)
     print(io, 'E', Groups.subscriptify(e.i), Groups.subscriptify(e.j))
-    !isone(e.val) && print(io, "^$(e.val)")
+    return !isone(e.val) && print(io, "^$(e.val)")
 end
 
-Base.:(==)(e::ElementaryMatrix{N}, f::ElementaryMatrix{N}) where {N} =
-    e.i == f.i && e.j == f.j && e.val == f.val
+function Base.:(==)(e::ElementaryMatrix{N}, f::ElementaryMatrix{N}) where {N}
+    return e.i == f.i && e.j == f.j && e.val == f.val
+end
 
-Base.hash(e::ElementaryMatrix, h::UInt) =
-    hash(typeof(e), hash((e.i, e.j, e.val), h))
+function Base.hash(e::ElementaryMatrix, h::UInt)
+    return hash(typeof(e), hash((e.i, e.j, e.val), h))
+end
 
-Base.inv(e::ElementaryMatrix{N}) where {N} =
-    ElementaryMatrix{N}(e.i, e.j, -e.val)
+function Base.inv(e::ElementaryMatrix{N}) where {N}
+    return ElementaryMatrix{N}(e.i, e.j, -e.val)
+end
 
 function matrix(e::ElementaryMatrix{N,T}) where {N,T}
     m = StaticArrays.MMatrix{N,N,T}(LinearAlgebra.I)
diff --git a/src/matrix_groups/eltary_symplectic.jl b/src/matrix_groups/eltary_symplectic.jl
index 91ab941..1f70a5c 100644
--- a/src/matrix_groups/eltary_symplectic.jl
+++ b/src/matrix_groups/eltary_symplectic.jl
@@ -3,7 +3,12 @@ struct ElementarySymplectic{N,T} <: Groups.GSymbol
     i::Int
     j::Int
     val::T
-    function ElementarySymplectic{N}(s::Symbol, i::Integer, j::Integer, val=1) where {N}
+    function ElementarySymplectic{N}(
+        s::Symbol,
+        i::Integer,
+        j::Integer,
+        val = 1,
+    ) where {N}
         @assert s ∈ (:A, :B)
         @assert iseven(N)
         n = N ÷ 2
@@ -19,7 +24,7 @@ end
 function Base.show(io::IO, s::ElementarySymplectic)
     i, j = Groups.subscriptify(s.i), Groups.subscriptify(s.j)
     print(io, s.symbol, i, j)
-    !isone(s.val) && print(io, "^$(s.val)")
+    return !isone(s.val) && print(io, "^$(s.val)")
 end
 
 _ind(s::ElementarySymplectic{N}) where {N} = (s.i, s.j)
@@ -41,21 +46,27 @@ function _dual_ind(N_half, i, j)
     return i, j
 end
 
-function Base.:(==)(s::ElementarySymplectic{N}, t::ElementarySymplectic{M}) where {N,M}
+function Base.:(==)(
+    s::ElementarySymplectic{N},
+    t::ElementarySymplectic{M},
+) where {N,M}
     N == M || return false
     s.symbol == t.symbol || return false
     s.val == t.val || return false
     return _ind(t) == _ind(s) || _ind(t) == _dual_ind(s)
 end
 
-Base.hash(s::ElementarySymplectic, h::UInt) =
-    hash(Set([_ind(s); _dual_ind(s)]), hash(s.symbol, hash(s.val, h)))
+function Base.hash(s::ElementarySymplectic, h::UInt)
+    return hash(Set([_ind(s); _dual_ind(s)]), hash(s.symbol, hash(s.val, h)))
+end
 
-LinearAlgebra.transpose(s::ElementarySymplectic{N}) where {N} =
-    ElementarySymplectic{N}(s.symbol, s.j, s.i, s.val)
+function LinearAlgebra.transpose(s::ElementarySymplectic{N}) where {N}
+    return ElementarySymplectic{N}(s.symbol, s.j, s.i, s.val)
+end
 
-Base.inv(s::ElementarySymplectic{N}) where {N} =
-    ElementarySymplectic{N}(s.symbol, s.i, s.j, -s.val)
+function Base.inv(s::ElementarySymplectic{N}) where {N}
+    return ElementarySymplectic{N}(s.symbol, s.i, s.j, -s.val)
+end
 
 function matrix(s::ElementarySymplectic{N,T}) where {N,T}
     @assert iseven(N)