diff --git a/python/src/SquareMatrix_doc.i.in b/python/src/SquareMatrix_doc.i.in
index d2f2908d2c2..972dd638114 100644
--- a/python/src/SquareMatrix_doc.i.in
+++ b/python/src/SquareMatrix_doc.i.in
@@ -32,7 +32,7 @@ Get or set terms
 [[ 1 ]
  [ 1 ]]
 
-Create an openturns matrix from a **square** numpy 2d-array (or matrix, or
+Create a matrix from a **square** Numpy 2d-array (or matrix, or
 2d-list)...
 
 >>> import numpy as np
@@ -299,3 +299,22 @@ Examples
 >>> M = ot.SquareMatrix([[1.0, 2.0], [3.0, 4.0]])
 >>> M.computeTrace()
 5.0"
+
+// ---------------------------------------------------------------------
+
+%feature("docstring") OT::SquareMatrix::inverse
+"Compute the inverse of the matrix.
+
+Returns
+-------
+inverseMatrix : :class:`~openturns.SquareMatrix`
+    The inverse of the matrix.
+
+Examples
+--------
+>>> import openturns as ot
+>>> M = ot.SquareMatrix([[1.0, 2.0, 3.0], [3.0, 2.0, 1.0], [2.0, 1.0, 3.0]])
+>>> print(12.0 * M.inverse())
+[[ -5  3  4 ]
+ [  7  3 -8 ]
+ [  1 -3  4 ]]"
diff --git a/python/src/SymmetricMatrix_doc.i.in b/python/src/SymmetricMatrix_doc.i.in
index 7840b440128..4a58d508e20 100644
--- a/python/src/SymmetricMatrix_doc.i.in
+++ b/python/src/SymmetricMatrix_doc.i.in
@@ -36,7 +36,7 @@ Get or set terms
 [[ 1 ]
  [ 2 ]]
 
-Create an openturns matrix from a **symmetric** numpy 2d-array (or matrix, or
+Create a matrix from a **symmetric** Numpy 2d-array (or matrix, or
 2d-list)...
 
 >>> import numpy as np
@@ -153,3 +153,22 @@ Examples
 
 %feature("docstring") OT::SymmetricMatrix::checkSymmetry
 "Check if the internal representation is really symmetric."
+
+// ---------------------------------------------------------------------
+
+%feature("docstring") OT::SymmetricMatrix::inverse
+"Compute the inverse of the matrix.
+
+Returns
+-------
+inverseMatrix : :class:`~openturns.SymmetricMatrix`
+    The inverse of the matrix.
+
+Examples
+--------
+>>> import openturns as ot
+>>> M = ot.SymmetricMatrix([[4.0, 2.0, 1.0], [2.0, 5.0, 3.0], [1.0, 3.0, 6.0]])
+>>> print(67.0 * M.inverse())
+[[  21  -9   1 ]
+ [  -9  23 -10 ]
+ [   1 -10  16 ]]"
diff --git a/python/test/t_SquareMatrix_std.py b/python/test/t_SquareMatrix_std.py
index ee599decdf1..8a9651071d9 100755
--- a/python/test/t_SquareMatrix_std.py
+++ b/python/test/t_SquareMatrix_std.py
@@ -1,6 +1,7 @@
 #! /usr/bin/env python
 
 import openturns as ot
+from openturns.testing import assert_almost_equal
 
 ot.TESTPREAMBLE()
 
@@ -126,3 +127,14 @@
 print("squareMatrix0 is empty = ", squareMatrix0.isEmpty())
 print("squareMatrix1 is empty = ", squareMatrix1.isEmpty())
 print("squareMatrix5 is empty = ", squareMatrix5.isEmpty())
+
+# Check inverse()
+squareMatrix6 = ot.SquareMatrix(
+    [[1.0, 2.0, 3.0], [3.0, 2.0, 1.0], [2.0, 1.0, 3.0]]
+    )
+squareMatrix7 = squareMatrix6.inverse()
+inverseReference = ot.SquareMatrix(
+    [[-5.0, 3.0, 4.0], [7.0, 3.0, -8.0], [1.0, -3.0, 4.0]]
+    )
+inverseReference /= 12.0
+assert_almost_equal(squareMatrix7, inverseReference)
diff --git a/python/test/t_SymmetricMatrix_std.py b/python/test/t_SymmetricMatrix_std.py
index 2956ce56bdc..638a3b77067 100755
--- a/python/test/t_SymmetricMatrix_std.py
+++ b/python/test/t_SymmetricMatrix_std.py
@@ -1,6 +1,7 @@
 #! /usr/bin/env python
 
 import openturns as ot
+from openturns.testing import assert_almost_equal
 
 ot.TESTPREAMBLE()
 
@@ -127,3 +128,10 @@
 print("symmetricMatrix0 is empty = ", symmetricMatrix0.isEmpty())
 print("symmetricMatrix1 is empty = ", symmetricMatrix1.isEmpty())
 print("symmetricMatrix5 is empty = ", symmetricMatrix5.isEmpty())
+
+# Check inverse()
+symmetricMatrix6 = ot.SymmetricMatrix([[4.0, 2.0, 1.0], [2.0, 5.0, 3.0], [1.0, 3.0, 6.0]])
+symmetricMatrix7 = symmetricMatrix6.inverse()
+inverseReference = ot.SymmetricMatrix([[21.0, -9.0, 1.0], [-9.0, 23.0, -10.0], [1.0, -10.0, 16.0]])
+inverseReference /= 67.0
+assert_almost_equal(symmetricMatrix7, inverseReference)