





from __future__ import annotations

from typing import Any




def   _SCREAMING_SNAKE_CASE      (	*snake_case_		:						list[list[int]]						):
     if all(_check_not_integer(snake_case_						) for m in matrix_s						):
          for i in matrix_s[1:]:
               _verify_matrix_sizes(matrix_s[0] ,     snake_case_						)
          return [[sum(snake_case_						) for t in zip(*snake_case_						)] for m in zip(*snake_case_						)]
     raise TypeError('''Expected a matrix, got int/list instead'''						)




def   _SCREAMING_SNAKE_CASE      (	snake_case_		:						list[list[int]] ,     snake_case_		:						list[list[int]]						):
     if (
         _check_not_integer(snake_case_						)
         and _check_not_integer(snake_case_						)
         and _verify_matrix_sizes(snake_case_ ,     snake_case_						)
     ):
          return [[i - j for i, j in zip(*snake_case_						)] for m in zip(snake_case_ ,     snake_case_						)]
     raise TypeError('''Expected a matrix, got int/list instead'''						)




def   _SCREAMING_SNAKE_CASE      (	snake_case_		:						list[list[int]] ,     snake_case_		:						int | float						):
     return [[x * n for x in row] for row in matrix]




def   _SCREAMING_SNAKE_CASE      (	snake_case_		:						list[list[int]] ,     snake_case_		:						list[list[int]]						):
     if _check_not_integer(snake_case_						) and _check_not_integer(snake_case_						):
          __magic_name__		,  __magic_name__				=       _verify_matrix_sizes(snake_case_ ,     snake_case_						)

     if cols[0] != rows[1]:
          __magic_name__				=       (
              '''Cannot multiply matrix of dimensions '''
              f'({rows[0]},{cols[0]}) and ({rows[1]},{cols[1]})'
          )
          raise ValueError(snake_case_						)
     return [
         [sum(m * n for m, n in zip(snake_case_ ,     snake_case_						)						) for j in zip(*snake_case_						)] for i in matrix_a
     ]




def   _SCREAMING_SNAKE_CASE      (	snake_case_		:						int						):
     __magic_name__				=       int(snake_case_						)
     return [[int(row == column						) for column in range(snake_case_						)] for row in range(snake_case_						)]




def   _SCREAMING_SNAKE_CASE      (	snake_case_		:						list[list[int]] ,     snake_case_		:						bool = True						):
     if _check_not_integer(snake_case_						):
          if return_map:
               return map(snake_case_ ,     zip(*snake_case_						)						)
          else:
               return list(map(snake_case_ ,     zip(*snake_case_						)						)						)
     raise TypeError('''Expected a matrix, got int/list instead'''						)




def   _SCREAMING_SNAKE_CASE      (	snake_case_		:						list[list[int]] ,     snake_case_		:						int ,     snake_case_		:						int						):
     __magic_name__				=       matrix[:row] + matrix[row + 1 :]
     return [row[:column] + row[column + 1 :] for row in minor]




def   _SCREAMING_SNAKE_CASE      (	snake_case_		:						list[list[int]]						):
     if len(snake_case_						) == 1:
          return matrix[0][0]

     return sum(
         x * determinant(minor(snake_case_ ,     0 ,     snake_case_						)						) * (-1) ** i
         for i, x in enumerate(matrix[0]						)						)




def   _SCREAMING_SNAKE_CASE      (	snake_case_		:						list[list[int]]						):
     __magic_name__				=       determinant(snake_case_						)
     if det == 0:
          return None

     __magic_name__				=       [
         [determinant(minor(snake_case_ ,     snake_case_ ,     snake_case_						)						) for j in range(len(snake_case_						)						)]
         for i in range(len(snake_case_						)						)
     ]

     __magic_name__				=       [
         [x * (-1) ** (row + col) for col, x in enumerate(matrix_minor[row]						)]
         for row in range(len(snake_case_						)						)
     ]
     __magic_name__				=       list(transpose(snake_case_						)						)
     return scalar_multiply(snake_case_ ,     1 / det						)




def   _SCREAMING_SNAKE_CASE      (	snake_case_		:						list[list[int]]						):
     return not isinstance(snake_case_ ,     snake_case_						) and not isinstance(matrix[0] ,     snake_case_						)




def   _SCREAMING_SNAKE_CASE      (	snake_case_		:						list[list[int]]						):
     return len(snake_case_						), len(matrix[0]						)




def   _SCREAMING_SNAKE_CASE      (	snake_case_		:						list[list[int]] ,     snake_case_		:						list[list[int]]						):
     __magic_name__				=       _shape(snake_case_						) + _shape(snake_case_						)
     if shape[0] != shape[3] or shape[1] != shape[2]:
          __magic_name__				=       (
              '''operands could not be broadcast together with shape '''
              f'({shape[0], shape[1]}), ({shape[2], shape[3]})'
          )
          raise ValueError(snake_case_						)
     return (shape[0], shape[2]), (shape[1], shape[3])




def   _SCREAMING_SNAKE_CASE      (	):
     __magic_name__				=       [[12, 10], [3, 9]]
     __magic_name__				=       [[3, 4], [7, 4]]
     __magic_name__				=       [[11, 12, 13, 14], [21, 22, 23, 24], [31, 32, 33, 34], [41, 42, 43, 44]]
     __magic_name__				=       [[3, 0, 2], [2, 0, -2], [0, 1, 1]]
     print(f'Add Operation, {add(snake_case_ ,     snake_case_						) = } \n'						)
     print(
         f'Multiply Operation, {multiply(snake_case_ ,     snake_case_						) = } \n' ,     )
     print(f'Identity: {identity(5						)}\n'						)
     print(f'Minor of {matrix_c} = {minor(snake_case_ ,     1 ,     2						)} \n'						)
     print(f'Determinant of {matrix_b} = {determinant(snake_case_						)} \n'						)
     print(f'Inverse of {matrix_d} = {inverse(snake_case_						)}\n'						)


if __name__ == "__main__":
    import doctest

    doctest.testmod()
    main()






def   _SCREAMING_SNAKE_CASE      (	snake_case_		:						int						):
     if not isinstance(snake_case_ ,     snake_case_						):
          __magic_name__				=       f'Input value of [number={number}] must be an integer'
          raise TypeError(snake_case_						)
     if number < 0 or number % 2 == 1:
          return False
     __magic_name__				=       int(number**0.5						)
     return number == number_sqrt * (number_sqrt + 1)


if __name__ == "__main__":
    import doctest

    doctest.testmod()