Added "Inverse of Matrix" Algorithm

matrix/inverse_of_matrix.py

@@ -0,0 +1,54 @@
+from decimal import *
+
+
+def inverse_of_matrix(matrix):
+    """
+    A matrix multiplied with its inverse gives the identity matrix.
+    This function finds the inverse of a 2x2 matrix.
+    If the determinant of a matrix is 0, its inverse does not exist.
+
+    Sources for fixing inaccurate float arithmetic:
+    https://stackoverflow.com/questions/6563058/how-do-i-use-accurate-float-arithmetic-in-python
+    https://docs.python.org/release/2.7/library/decimal.html#module-decimal
+
+    >>> inverse_of_matrix([[2, 5], [2, 0]])
+    [[0.0, 0.5], [0.2, -0.2]]
+    >>> inverse_of_matrix([[2.5, 5], [1, 2]])
+    'Does not exist'
+    >>> inverse_of_matrix([[12, -16], [-9, 0]])
+    [[0.0, -0.1111111111111111], [-0.0625, -0.08333333333333333]]
+    >>> inverse_of_matrix([[12, 3], [16, 8]])
+    [[0.16666666666666666, -0.0625], [-0.3333333333333333, 0.25]]
+    >>> inverse_of_matrix([[10, 9], [2, 2.5]])
+    [[1.0, -4.5], [-1.0, 5.0]]
+    """
+
+    determinant = Decimal(matrix[0][0]) * Decimal(matrix[1][1]) - Decimal(
+        matrix[1][0]
+    ) * Decimal(
+        matrix[0][1]
+    )  # Finds the determinant of the matrix
+    if determinant != 0:
+        inverse = []
+        matrix_with_swapped_pos = (
+            [] + matrix
+        )  # Creates a copy of the matrix and swaps the positions of the elements
+        matrix_with_swapped_pos[0][0], matrix_with_swapped_pos[1][1] = (
+            matrix[1][1],
+            matrix[0][0],
+        )
+        matrix_with_swapped_pos[1][0], matrix_with_swapped_pos[0][1] = (
+            0 - matrix[1][0],
+            0 - matrix[0][1],
+        )
+        for row1 in matrix_with_swapped_pos:
+            inverse.append(
+                [float(Decimal(num) / determinant) for num in row1]
+            )  # Finds the inverse of the matrix
+        for row2 in inverse:
+            for index in range(len(row2)):  # Replaces the -0.0's with 0.0's
+                if row2[index] == -0.0:
+                    row2[index] = 0.0
+        return inverse
+    else:
+        return 'Does not exist'