





from __future__ import annotations

from typing import Any





def     lowerCamelCase__  (  *UpperCamelCase__      :							List[str]    )      ->			Tuple:



					'''simple docstring'''




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





def     lowerCamelCase__  (  UpperCamelCase__      :							str							,     UpperCamelCase__      :							Union[str, Any]    )      ->			Optional[Any]:



					'''simple docstring'''




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





def     lowerCamelCase__  (  UpperCamelCase__      :							Optional[int]							,     UpperCamelCase__      :							Optional[int]    )      ->			List[Any]:



					'''simple docstring'''




					return [[x * n for x in row] for row in matrix]





def     lowerCamelCase__  (  UpperCamelCase__      :							List[Any]							,     UpperCamelCase__      :							Optional[int]    )      ->			List[str]:



					'''simple docstring'''




					if _check_not_integer(UpperCamelCase__    ) and _check_not_integer(UpperCamelCase__    ):
										_snake_case						=					_verify_matrix_sizes(UpperCamelCase__							,     UpperCamelCase__    )

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





def     lowerCamelCase__  (  UpperCamelCase__      :							int    )      ->			Optional[Any]:



					'''simple docstring'''




					_snake_case						=					int(UpperCamelCase__    )
					return [[int(row == column    ) for column in range(UpperCamelCase__    )] for row in range(UpperCamelCase__    )]





def     lowerCamelCase__  (  UpperCamelCase__      :							Optional[Any]							,     UpperCamelCase__      :							List[str] = True    )      ->			Any:



					'''simple docstring'''




					if _check_not_integer(UpperCamelCase__    ):
										if return_map:
															return map(UpperCamelCase__							,     zip(*UpperCamelCase__    )    )
										else:
															return list(map(UpperCamelCase__							,     zip(*UpperCamelCase__    )    )    )
					raise TypeError('Expected a matrix, got int/list instead'    )





def     lowerCamelCase__  (  UpperCamelCase__      :							int							,     UpperCamelCase__      :							str							,     UpperCamelCase__      :							int    )      ->			Optional[Any]:



					'''simple docstring'''




					_snake_case						=					matrix[:row] + matrix[row + 1 :]
					return [row[:column] + row[column + 1 :] for row in minor]





def     lowerCamelCase__  (  UpperCamelCase__      :							List[str]    )      ->			Dict:



					'''simple docstring'''




					if len(UpperCamelCase__    ) == 1:
										return matrix[0][0]

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





def     lowerCamelCase__  (  UpperCamelCase__      :							Optional[int]    )      ->			Any:



					'''simple docstring'''




					_snake_case						=					determinant(UpperCamelCase__    )
					if det == 0:
										return None

					_snake_case						=					[
					    [determinant(minor(UpperCamelCase__							,     UpperCamelCase__							,     UpperCamelCase__    )    ) for j in range(len(UpperCamelCase__    )    )]
					    for i in range(len(UpperCamelCase__    )    )
					]

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





def     lowerCamelCase__  (  UpperCamelCase__      :							Optional[Any]    )      ->			Optional[int]:



					'''simple docstring'''




					return not isinstance(UpperCamelCase__							,     UpperCamelCase__    ) and not isinstance(matrix[0]							,     UpperCamelCase__    )





def     lowerCamelCase__  (  UpperCamelCase__      :							Dict    )      ->			Optional[Any]:



					'''simple docstring'''




					return len(UpperCamelCase__    ), len(matrix[0]    )





def     lowerCamelCase__  (  UpperCamelCase__      :							Tuple							,     UpperCamelCase__      :							List[str]    )      ->			Dict:



					'''simple docstring'''




					_snake_case						=					_shape(UpperCamelCase__    ) + _shape(UpperCamelCase__    )
					if shape[0] != shape[3] or shape[1] != shape[2]:
										_snake_case						=					(
										    '''operands could not be broadcast together with shape '''
										    F'''({shape[0], shape[1]}), ({shape[2], shape[3]})'''
										)
										raise ValueError(UpperCamelCase__    )
					return (shape[0], shape[2]), (shape[1], shape[3])





def     lowerCamelCase__  (  )      ->			Any:



					'''simple docstring'''




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


if __name__ == "__main__":
					import doctest

					doctest.testmod()
					main()









"""simple docstring"""





from __future__ import annotations

from enum import Enum, unique
from typing import TypeVar

# Create a generic variable that can be 'Enum', or any subclass.
_lowercase						   =     TypeVar("""T""", bound="""Enum""")

@unique
class    __lowercase							(      snake_case_						):


				'''simple docstring'''


				_lowerCAmelCase						      =80
				_lowerCAmelCase						      =70
				_lowerCAmelCase						      =60
				_lowerCAmelCase						      =50
				_lowerCAmelCase						      =40
				_lowerCAmelCase						      =30
				_lowerCAmelCase						      =20
				_lowerCAmelCase						      =10







@unique
class    __lowercase							(      snake_case_						):


				'''simple docstring'''


				_lowerCAmelCase						      =24
				_lowerCAmelCase						      =21
				_lowerCAmelCase						      =18
				_lowerCAmelCase						      =15
				_lowerCAmelCase						      =12
				_lowerCAmelCase						      =9
				_lowerCAmelCase						      =6
				_lowerCAmelCase						      =3
				_lowerCAmelCase						      =2
				_lowerCAmelCase						      =1
				_lowerCAmelCase						      =-1
				_lowerCAmelCase						      =-2
				_lowerCAmelCase						      =-3
				_lowerCAmelCase						      =-6
				_lowerCAmelCase						      =-9
				_lowerCAmelCase						      =-12
				_lowerCAmelCase						      =-15
				_lowerCAmelCase						      =-18
				_lowerCAmelCase						      =-21
				_lowerCAmelCase						      =-24

				@classmethod
				def    _lowerCamelCase       ( cls :  type[T]   ):
										return {unit.name: unit.value for unit in cls if unit.value > 0}





				@classmethod
				def    _lowerCamelCase       ( cls :  type[T]   ):
										return {unit.name: unit.value for unit in cls if unit.value < 0}







def 		lowerCAmelCase				(			lowerCamelCase		):
						'''simple docstring'''


						snake_case__							:       List[Any]				      =       SIUnit.get_positive() if value > 0 else SIUnit.get_negative()
						for name_prefix, value_prefix in prefixes.items():
												snake_case__							:       Optional[int]				      =       value / (10**value_prefix)
												if numerical_part > 1:
																		return f'''{numerical_part!s} {name_prefix}'''
						return str(lowerCamelCase		)

def 		lowerCAmelCase				(			lowerCamelCase		):
						'''simple docstring'''


						for prefix in BinaryUnit:
												snake_case__							:       int				      =       value / (2**prefix.value)
												if numerical_part > 1:
																		return f'''{numerical_part!s} {prefix.name}'''
						return str(lowerCamelCase		)


if __name__ == "__main__":
							import doctest

							doctest.testmod()


