Added "Inverse of Matrix" Algorithm (TheAlgorithms#2209)

* Added "Inverse of Matrix" Algorithm

* Small quotation marks change

* Update inverse_of_matrix.py

* Updated doctests

* Update inverse_of_matrix.py

* Add type hints

* swaped --> swapped

Co-authored-by: Christian Clauss <[email protected]>

matrix/inverse_of_matrix.py

@@ -0,0 +1,39 @@
+from decimal import Decimal
+from typing import List
+
+
+def inverse_of_matrix(matrix: List[List[float]]) -> List[List[float]]:
+    """
+    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/3/library/decimal.html
+
+    >>> inverse_of_matrix([[2, 5], [2, 0]])
+    [[0.0, 0.5], [0.2, -0.2]]
+    >>> inverse_of_matrix([[2.5, 5], [1, 2]])
+    Traceback (most recent call last):
+    ...
+    ValueError: This matrix has no inverse.
+    >>> 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, 5], [3, 2.5]])
+    [[0.25, -0.5], [-0.3, 1.0]]
+    """
+
+    D = Decimal  # An abbreviation to be conciseness
+    # Calculate the determinant of the matrix
+    determinant = D(matrix[0][0]) * D(matrix[1][1]) - D(matrix[1][0]) * D(matrix[0][1])
+    if determinant == 0:
+        raise ValueError("This matrix has no inverse.")
+    # Creates a copy of the matrix with swapped positions of the elements
+    swapped_matrix = [[0.0, 0.0], [0.0, 0.0]]
+    swapped_matrix[0][0], swapped_matrix[1][1] = matrix[1][1], matrix[0][0]
+    swapped_matrix[1][0], swapped_matrix[0][1] = -matrix[1][0], -matrix[0][1]
+    # Calculate the inverse of the matrix
+    return [[float(D(n) / determinant) or 0.0 for n in row] for row in swapped_matrix]