From c6267b944d157ffbc0e243e5a1575a4c77c08e42 Mon Sep 17 00:00:00 2001
From: Anoush Mudaliar <anoush.mudaliar@gmail.com>
Date: Tue, 26 Mar 2019 21:59:25 -0400
Subject: [PATCH 1/3] added matrix minor

---
 matrix/matrix_multiplication_addition.py | 6 ++++++
 1 file changed, 6 insertions(+)

diff --git a/matrix/matrix_multiplication_addition.py b/matrix/matrix_multiplication_addition.py
index c387c43d4a85..93bb8f5dbc07 100644
--- a/matrix/matrix_multiplication_addition.py
+++ b/matrix/matrix_multiplication_addition.py
@@ -24,10 +24,16 @@ def multiply(matrix_a, matrix_b):
         matrix_c.append(list_1)
     return matrix_c
 
+def minor(matrix, row, column):
+    minor = matrix[:row] + matrix[row + 1:]
+    minor = [row[:column] + row[column + 1:] for row in minor]
+    return minor
 
 def main():
     matrix_a = [[12, 10], [3, 9]]
     matrix_b = [[3, 4], [7, 4]]
+    matrix_c = [[11, 12, 13, 14], [21, 22, 23, 24], [31, 32, 33, 34], [41, 42, 43, 44]]
+    print(minor(matrix_c , 1 , 2))
     print(add(matrix_a, matrix_b))
     print(multiply(matrix_a, matrix_b))
 

From 9583907039d50e3377334a930cd42806f64ae397 Mon Sep 17 00:00:00 2001
From: Anoush Mudaliar <anoush.mudaliar@gmail.com>
Date: Tue, 26 Mar 2019 22:26:39 -0400
Subject: [PATCH 2/3] added matrix determinant

---
 matrix/matrix_multiplication_addition.py | 13 +++++++++++--
 1 file changed, 11 insertions(+), 2 deletions(-)

diff --git a/matrix/matrix_multiplication_addition.py b/matrix/matrix_multiplication_addition.py
index 93bb8f5dbc07..a1de82181d1d 100644
--- a/matrix/matrix_multiplication_addition.py
+++ b/matrix/matrix_multiplication_addition.py
@@ -29,14 +29,23 @@ def minor(matrix, row, column):
     minor = [row[:column] + row[column + 1:] for row in minor]
     return minor
 
+def determinant(matrix):
+    if len(matrix) == 1: return matrix[0][0]
+    
+    res = 0
+    for x in range(len(matrix)):
+        res += matrix[0][x] * determinant(minor(matrix , 0 , x)) * (-1) ** x
+    return res
+
 def main():
     matrix_a = [[12, 10], [3, 9]]
     matrix_b = [[3, 4], [7, 4]]
     matrix_c = [[11, 12, 13, 14], [21, 22, 23, 24], [31, 32, 33, 34], [41, 42, 43, 44]]
-    print(minor(matrix_c , 1 , 2))
+
     print(add(matrix_a, matrix_b))
     print(multiply(matrix_a, matrix_b))
-
+    print(minor(matrix_c , 1 , 2))
+    print(determinant(matrix_b))
 
 if __name__ == '__main__':
     main()

From 87314d1d63d04d10418a0339d980303682399740 Mon Sep 17 00:00:00 2001
From: Anoush Mudaliar <anoush.mudaliar@gmail.com>
Date: Wed, 27 Mar 2019 11:28:39 -0400
Subject: [PATCH 3/3] added inverse,scalar multiply, identity, transpose

---
 matrix/matrix_multiplication_addition.py | 24 ++++++++++++++++++++++++
 1 file changed, 24 insertions(+)

diff --git a/matrix/matrix_multiplication_addition.py b/matrix/matrix_multiplication_addition.py
index a1de82181d1d..dd50db729e43 100644
--- a/matrix/matrix_multiplication_addition.py
+++ b/matrix/matrix_multiplication_addition.py
@@ -10,6 +10,8 @@ def add(matrix_a, matrix_b):
         matrix_c.append(list_1)
     return matrix_c
 
+def scalarMultiply(matrix , n):
+    return [[x * n for x in row] for row in matrix]
 
 def multiply(matrix_a, matrix_b):
     matrix_c = []
@@ -24,6 +26,12 @@ def multiply(matrix_a, matrix_b):
         matrix_c.append(list_1)
     return matrix_c
 
+def identity(n):
+    return [[int(row == column) for column in range(n)] for row in range(n)] 
+
+def transpose(matrix):
+    return map(list , zip(*matrix))
+
 def minor(matrix, row, column):
     minor = matrix[:row] + matrix[row + 1:]
     minor = [row[:column] + row[column + 1:] for row in minor]
@@ -37,15 +45,31 @@ def determinant(matrix):
         res += matrix[0][x] * determinant(minor(matrix , 0 , x)) * (-1) ** x
     return res
 
+def inverse(matrix):
+    det = determinant(matrix)
+    if det == 0: return None
+
+    matrixMinor = [[] for _ in range(len(matrix))]
+    for i in range(len(matrix)):
+        for j in range(len(matrix)):
+            matrixMinor[i].append(determinant(minor(matrix , i , j)))
+    
+    cofactors = [[x * (-1) ** (row + col) for col, x in enumerate(matrixMinor[row])] for row in range(len(matrix))]
+    adjugate = transpose(cofactors)
+    return scalarMultiply(adjugate , 1/det)
+
 def main():
     matrix_a = [[12, 10], [3, 9]]
     matrix_b = [[3, 4], [7, 4]]
     matrix_c = [[11, 12, 13, 14], [21, 22, 23, 24], [31, 32, 33, 34], [41, 42, 43, 44]]
+    matrix_d = [[3, 0, 2], [2, 0, -2], [0, 1, 1]]
 
     print(add(matrix_a, matrix_b))
     print(multiply(matrix_a, matrix_b))
+    print(identity(5))
     print(minor(matrix_c , 1 , 2))
     print(determinant(matrix_b))
+    print(inverse(matrix_d))
 
 if __name__ == '__main__':
     main()