diff --git a/docs/src/matrix.md b/docs/src/matrix.md
index f46fb6f78c..9a549d63af 100644
--- a/docs/src/matrix.md
+++ b/docs/src/matrix.md
@@ -566,7 +566,8 @@ julia> c = M[1, 1]
 ### Transpose
 
 ```@docs
-transpose(::MatrixElem{T}) where T <: RingElement
+transpose(::MatrixElem)
+transpose!(::MatrixElem)
 ```
 
 ### Submatrices
diff --git a/src/Matrix.jl b/src/Matrix.jl
index a5fe96ddaf..a5eae17c40 100644
--- a/src/Matrix.jl
+++ b/src/Matrix.jl
@@ -1482,9 +1482,9 @@ end
 
 
 @doc raw"""
-    transpose(x::MatrixElem{T}) where T <: NCRingElement
+    transpose(x::MatrixElem)
 
-Return the transpose of the given matrix.
+Return the transpose of `x`.
 
 # Examples
 
@@ -1508,9 +1508,43 @@ julia> B = transpose(A)
 
 ```
 """
-transpose(x::MatrixElem{T}) where T <: NCRingElement
+function transpose(x::MatrixElem)
+  z = similar(base_ring(x), ncols(x), nrows(x))
+  return transpose!(z, x)
+end
+
+@doc raw"""
+    transpose!(x::MatrixElem)
+    transpose!(z::T, x::T) where T <: MatrixElem
+
+Return the transpose of `x`, possibly modifying the object `z` in the process.
+Aliasing is permitted.
+The unary version may modify `x` in-place (but this is not always possible).
+"""
+function transpose!(x::MatrixElem)
+  if is_square(x)
+    # square matrix, so we can transpose it in-place
+    n = nrows(x)
+    for i in 1:n
+      for j in i+1:n
+        x[i, j], x[j, i] = x[j, i], x[i, j]
+      end
+    end
+    return x
+  end
+  # we have no generic way to change the dimensions of x, so instead we
+  # delegate to the two argument version of transpose!
+  z = similar(base_ring(x), ncols(x), nrows(x))
+  return transpose!(z, x)
+end
+
+function transpose!(z::T, x::T) where T <: MatrixElem
+  for i in 1:nrows(x), j in 1:ncols(x)
+    z[j, i] = x[i, j]
+  end
+  return z
+end
 
-transpose!(A::MatrixElem) = transpose(A)
 
 ###############################################################################
 #
diff --git a/src/exports.jl b/src/exports.jl
index 11dbc97cb6..ee48a02ab0 100644
--- a/src/exports.jl
+++ b/src/exports.jl
@@ -554,6 +554,8 @@ export total_degree
 export total_ring_of_fractions
 export tr
 export trailing_coefficient
+export transpose
+export transpose!
 export truncate
 export typed_hcat
 export typed_hvcat
diff --git a/test/Rings-conformance-tests.jl b/test/Rings-conformance-tests.jl
index 3e45769ee7..eb74e3cbd0 100644
--- a/test/Rings-conformance-tests.jl
+++ b/test/Rings-conformance-tests.jl
@@ -805,10 +805,23 @@ function test_MatSpace_interface(S::MatSpace; reps = 20)
 
             t = transpose(a)
             @test t isa ST
+            @test base_ring(t) == base_ring(a)
             @test nrows(t) == ncols(S)
             @test ncols(t) == nrows(S)
             @test transpose(t) == a
             @test a == A
+
+            t = transpose!(deepcopy(a))
+            @test t isa ST
+            @test base_ring(t) == base_ring(a)
+            @test t == transpose(a)
+
+            z = zero_matrix(R, ncols(a), nrows(a))
+            t = transpose!(z, a)
+            @test t isa ST
+            @test base_ring(t) == base_ring(a)
+            @test t == transpose(a)
+            @test a == A
          end
       end