diff --git a/two_qubit_simulator/initial_state.py b/two_qubit_simulator/initial_state.py
new file mode 100644
index 0000000..58b28f3
--- /dev/null
+++ b/two_qubit_simulator/initial_state.py
@@ -0,0 +1,14 @@
+def random_quantum_state():
+ """
+ Returns a random qubit state.
+ The qubit will be a column vector with complex elements a+ib and c+id. 
+ a,b,c and d are randomly chosen. The norm ensures the state is normalised. 
+ """
+ import numpy as np 
+ import random
+ a = random.random()
+ b = random.random()
+ c = random.random()
+ d = random.random()
+ norm = np.sqrt (( a + 1j * b) * (a - 1j * b) + (c + 1j * d) * (c - 1j * d))
+ return np.array([[a + 1j * b] , [c + 1j * d] ]) / norm
\ No newline at end of file
diff --git a/two_qubit_simulator/quantum_gates/hadamard.py b/two_qubit_simulator/quantum_gates/hadamard.py
index 2dfcffc..82a2269 100644
--- a/two_qubit_simulator/quantum_gates/hadamard.py
+++ b/two_qubit_simulator/quantum_gates/hadamard.py
@@ -6,4 +6,4 @@
 
 class Hadamard(QuantumGate):
     """ Implements the Hadamard gate """
-    pass
+   def __init__(self,elements)
diff --git a/two_qubit_simulator/quantum_gates/quantum_gate.py b/two_qubit_simulator/quantum_gates/quantum_gate.py
index c15f811..f6ac763 100644
--- a/two_qubit_simulator/quantum_gates/quantum_gate.py
+++ b/two_qubit_simulator/quantum_gates/quantum_gate.py
@@ -27,7 +27,7 @@ def __init__(self, unitary_operator, symbol=None):
 
     def assert_operation_is_unitary(self):
         """ Checks that the input unitary operator is unitary """
-        pass
+        assert unitary_operator.dot(conjugate_transpose(unitary_operator))== np.eye(4)
 
     def __call__(self, register):
         """ Apply the gate to a given qubit register. See apply_register method """
diff --git a/two_qubit_simulator/utilties.py b/two_qubit_simulator/utilties.py
new file mode 100644
index 0000000..83240b1
--- /dev/null
+++ b/two_qubit_simulator/utilties.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)
+    )
\ No newline at end of file