diff --git a/numpy_questions.py b/numpy_questions.py
index 07a10c1..c22ff14 100644
--- a/numpy_questions.py
+++ b/numpy_questions.py
@@ -15,6 +15,7 @@
 This will be enforced with `flake8`. You can check that there is no flake8
 errors by calling `flake8` at the root of the repo.
 """
+
 import numpy as np
 
 
@@ -29,7 +30,7 @@ def max_index(X):
     Returns
     -------
     (i, j) : tuple(int)
-        The row and columnd index of the maximum.
+        The row and column index of the maximum.
 
     Raises
     ------
@@ -37,10 +38,17 @@ def max_index(X):
         If the input is not a numpy array or
         if the shape is not 2D.
     """
-    i = 0
-    j = 0
+    # Check if X is a numpy array
+    if not isinstance(X, np.ndarray):
+        raise ValueError("Input must be a numpy array.")
+
+    # Check if X is 2D
+    if X.ndim != 2:
+        raise ValueError("Input array must be 2-dimensional.")
 
-    # TODO
+    # Find the index of the maximum element
+    flat_index = np.argmax(X)  # Get the flattened index of the max element
+    i, j = divmod(flat_index, X.shape[1])
 
     return i, j
 
@@ -62,6 +70,11 @@ def wallis_product(n_terms):
     pi : float
         The approximation of order `n_terms` of pi using the Wallis product.
     """
-    # XXX : The n_terms is an int that corresponds to the number of
-    # terms in the product. For example 10000.
-    return 0.
+
+    product = 1.0
+    for i in range(1, n_terms + 1):
+        numerator = 4 * i**2
+        denominator = (4 * i**2) - 1
+        product *= numerator / denominator
+
+    return product * 2