diff --git a/src/Matrix.jl b/src/Matrix.jl
index b5fc74af47..b269b0a959 100644
--- a/src/Matrix.jl
+++ b/src/Matrix.jl
@@ -48,13 +48,42 @@ function _check_bases(a, b)
   return nothing
 end
 
-function (s::MatSpace{T})(a::M) where {T, M <: MatrixElem{T}}
+# create a zero matrix
+function (s::MatSpace{T})() where {T <: NCRingElement}
+  return zero_matrix(base_ring(s), nrows(s), ncols(s))::eltype(s)
+end
+
+function (s::MatSpace{T})(a::MatrixElem{T}) where {T <: NCRingElement}
   _check_dim(nrows(s), ncols(s), a)
   _check_bases(s, a)
   a isa eltype(s) && return a
-  b = eltype(s)(a)
-  b.base_ring = base_ring(s)
-  return b
+  M = s()  # zero matrix
+  R = base_ring(s)
+  if R == base_ring(a)
+    for i = 1:nrows(s)
+      for j = 1:ncols(s)
+        M[i, j] = a[i, j]
+      end
+    end
+  else
+    for i = 1:nrows(s)
+      for j = 1:ncols(s)
+        M[i, j] = R(a[i, j])
+      end
+    end
+  end
+  return M
+end
+
+# create a matrix with b on the diagonal
+function (s::MatSpace)(b::NCRingElement)
+  M = s()  # zero matrix
+  R = base_ring(s)
+  rb = R(b)
+  for i in 1:min(nrows(s), ncols(s))
+    M[i, i] = rb
+  end
+  return M
 end
 
 _checkbounds(i::Int, j::Int) = 1 <= j <= i
@@ -6577,10 +6606,18 @@ function matrix(R::NCRing, arr::AbstractMatrix{T}) where {T}
 end
 
 function matrix(R::NCRing, arr::MatElem)
-    return map_entries(R, arr)
+   return map_entries(R, arr)
+end
+
+function matrix(R::NCRing, arr::MatRingElem)
+   return matrix_space(R, nrows(arr), ncols(arr))(arr)
+end
+
+function matrix(mat::MatrixElem{T}) where {T<:NCRingElement}
+   return matrix(base_ring(mat), mat)
 end
 
-function matrix(arr::AbstractMatrix{T}) where {T<:NCRingElem}
+function matrix(arr::AbstractMatrix{T}) where {T<:NCRingElement}
    r, c = size(arr)
    (r < 0 || c < 0) && error("Array must be non-empty")
    R = parent(arr[1, 1])
@@ -6588,11 +6625,11 @@ function matrix(arr::AbstractMatrix{T}) where {T<:NCRingElem}
    return matrix(R, arr)
 end
 
-function matrix(arr::AbstractVector{T}) where {T<:NCRingElem}
+function matrix(arr::AbstractVector{T}) where {T<:NCRingElement}
    return matrix(reshape(arr, length(arr), 1))
 end
 
-function matrix(arr::Vector{Vector{T}}) where {T<:NCRingElem}
+function matrix(arr::Vector{Vector{T}}) where {T<:NCRingElement}
     return matrix(permutedims(reduce(hcat, arr), (2, 1)))
 end
 
diff --git a/src/generic/MatRing.jl b/src/generic/MatRing.jl
index 67c68142af..23c18760ee 100644
--- a/src/generic/MatRing.jl
+++ b/src/generic/MatRing.jl
@@ -146,11 +146,42 @@ function (a::MatRing{T})(b::S) where {S <: NCRingElement, T <: NCRingElement}
    return z
 end
 
+# to resolve ambiguity for MatRing{MatRing{...}}
+function (a::MatRing{T})(b::T) where {S <: NCRingElement, T <: MatRingElem{S}}
+   R = base_ring(a)
+   entries = Matrix{T}(undef, a.n, a.n)
+   rb = R(b)
+   for i = 1:a.n
+      for j = 1:a.n
+         if i != j
+            entries[i, j] = zero(R)
+         else
+            entries[i, j] = rb
+         end
+      end
+   end
+   z = MatRingElem{T}(R, entries)
+   return z
+end
+
 function (a::MatRing{T})(b::MatRingElem{T}) where {T <: NCRingElement}
    parent(b) != a && error("Unable to coerce matrix")
    return b
 end
 
+function (a::MatRing{T})(b::MatrixElem{S}) where {S <: NCRingElement, T <: NCRingElement}
+   R = base_ring(a)
+   _check_dim(nrows(a), ncols(a), b)
+   entries = Matrix{T}(undef, nrows(a), ncols(a))
+   for i = 1:nrows(a)
+      for j = 1:ncols(a)
+         entries[i, j] = R(b[i, j])
+      end
+   end
+   z = MatRingElem{T}(R, entries)
+   return z
+end
+
 function (a::MatRing{T})(b::Matrix{S}) where {S <: NCRingElement, T <: NCRingElement}
    R = base_ring(a)
    _check_dim(a.n, a.n, b)
diff --git a/src/generic/Matrix.jl b/src/generic/Matrix.jl
index 800564ea22..844924d50e 100644
--- a/src/generic/Matrix.jl
+++ b/src/generic/Matrix.jl
@@ -148,21 +148,7 @@ end
 #
 ###############################################################################
 
-# create a zero matrix
-function (a::Generic.MatSpace{T})() where {T <: NCRingElement}
-   return zero_matrix(base_ring(a), nrows(a), ncols(a))::dense_matrix_type(T)
-end
 
-# create a matrix with b on the diagonal
-function (a::Generic.MatSpace)(b::NCRingElement)
-   M = a()  # zero matrix
-   R = base_ring(a)
-   rb = R(b)
-   for i in 1:min(nrows(a), ncols(a))
-      M[i, i] = rb
-   end
-   return M
-end
 
 # convert a Julia matrix
 function (a::Generic.MatSpace{T})(b::AbstractMatrix{S}) where {T <: NCRingElement, S}
diff --git a/test/Matrix-test.jl b/test/Matrix-test.jl
index dd206c6118..e9d24f536b 100644
--- a/test/Matrix-test.jl
+++ b/test/Matrix-test.jl
@@ -112,6 +112,26 @@ end
     @test T == matrix(QQ, [42 0 0; 0 42 0; 0 0 42])
 end
 
+@testset "Matrix.conversion" begin
+  U, t = polynomial_ring(QQ, "t")
+
+  R = matrix_ring(U, 2)
+  S = matrix_space(U, 2, 2)
+  a = U.([1 2; t^2 (t-1)]) # Matrix
+  Ra = R(a) # MatRingElem
+  Sa = S(a) # MatElem
+  @test Ra == R(Ra)
+  @test Ra == R(Sa)
+  @test Sa == S(Sa)
+  @test Sa == S(Ra)
+  @test matrix(Ra) == Sa
+  @test matrix(U, Ra) == Ra
+  @test matrix(Sa) == Sa
+  @test matrix(U, Sa) == Sa
+  @test Matrix(Ra) == a
+  @test Matrix(Sa) == a
+end
+
 @testset "Strassen" begin
    S = matrix(QQ, rand(-10:10, 100, 100))
    T = S*S