diff --git a/.cache/v/cache/lastfailed b/.cache/v/cache/lastfailed
new file mode 100644
index 0000000..9e26dfe
--- /dev/null
+++ b/.cache/v/cache/lastfailed
@@ -0,0 +1 @@
+{}
\ No newline at end of file
diff --git a/tests/test_utilities.py b/tests/test_utilities.py
new file mode 100644
index 0000000..eb3777b
--- /dev/null
+++ b/tests/test_utilities.py
@@ -0,0 +1,20 @@
+"""
+# test_utilities.py
+Test the functions in the utilities module
+"""
+import numpy as np
+from two_qubit_simulator import conjugate_transpose
+
+def test_conjugate_transpose():
+    # Test with real-valued array
+    test_array_1 = np.array([[1, 2], [3, 4]])
+    assert np.allclose(
+        conjugate_transpose(test_array_1),
+        np.array([[1, 3], [2, 4]])
+    )
+    # Test with complex-valued array
+    test_array_1 = np.array([[1j, 2], [1j, 4]])
+    assert np.allclose(
+        conjugate_transpose(test_array_1),
+        np.array([[-1j, -1j], [2, 4]])
+    )
diff --git a/two_qubit_simulator/__init__.py b/two_qubit_simulator/__init__.py
index 942b51f..e925c73 100644
--- a/two_qubit_simulator/__init__.py
+++ b/two_qubit_simulator/__init__.py
@@ -2,3 +2,4 @@
 Initialise the two_qubit_simulator module.
 Add import statements from auxilirary modules here.
 """
+from .utilities import conjugate_transpose
\ No newline at end of file
diff --git a/two_qubit_simulator/utilities.py b/two_qubit_simulator/utilities.py
new file mode 100644
index 0000000..09fc142
--- /dev/null
+++ b/two_qubit_simulator/utilities.py
@@ -0,0 +1,22 @@
+"""
+# utilities.py
+Contains utility functions for the two_qubit_simulator module
+"""
+import numpy as np
+
+def conjugate_transpose(array):
+    """ Calculates the conjugate transpose of an array
+
+        Parameters
+        -------
+        array : numpy ndarray
+            The array to be transposed
+        
+        Returns
+        -------
+        numpy ndarray
+            The conjugate transpose of the input array
+    """
+    return np.conjugate(
+        np.transpose(array)
+    )