






"""simple docstring"""
from __future__ import annotations

from typing import Any






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






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






def        lowerCamelCase_  (						_lowerCamelCase			,   _lowerCamelCase				):
 return [[x * n for x in row] for row in matrix]






def        lowerCamelCase_  (						_lowerCamelCase			,   _lowerCamelCase				):
 if _check_not_integer(_lowerCamelCase				) and _check_not_integer(_lowerCamelCase				):
  lowerCamelCase__				,     lowerCamelCase__     :			Dict     				=						_verify_matrix_sizes(_lowerCamelCase			,   _lowerCamelCase				)

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






def        lowerCamelCase_  (						_lowerCamelCase				):
 lowerCamelCase__     :			Union[str, Any]     				=						int(_lowerCamelCase				)
 return [[int(row == column				) for column in range(_lowerCamelCase				)] for row in range(_lowerCamelCase				)]






def        lowerCamelCase_  (						_lowerCamelCase			,   _lowerCamelCase = True				):
 if _check_not_integer(_lowerCamelCase				):
  if return_map:
   return map(_lowerCamelCase			,   zip(*_lowerCamelCase				)				)
  else:
   return list(map(_lowerCamelCase			,   zip(*_lowerCamelCase				)				)				)
 raise TypeError('Expected a matrix, got int/list instead'				)






def        lowerCamelCase_  (						_lowerCamelCase			,   _lowerCamelCase			,   _lowerCamelCase				):
 lowerCamelCase__     :			str     				=						matrix[:row] + matrix[row + 1 :]
 return [row[:column] + row[column + 1 :] for row in minor]






def        lowerCamelCase_  (						_lowerCamelCase				):
 if len(_lowerCamelCase				) == 1:
  return matrix[0][0]

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






def        lowerCamelCase_  (						_lowerCamelCase				):
 lowerCamelCase__     :			Dict     				=						determinant(_lowerCamelCase				)
 if det == 0:
  return None

 lowerCamelCase__     :			Dict     				=						[
     [determinant(minor(_lowerCamelCase			,   _lowerCamelCase			,   _lowerCamelCase				)				) for j in range(len(_lowerCamelCase				)				)]
     for i in range(len(_lowerCamelCase				)				)
 ]

 lowerCamelCase__     :			List[str]     				=						[
     [x * (-1) ** (row + col) for col, x in enumerate(matrix_minor[row]				)]
     for row in range(len(_lowerCamelCase				)				)
 ]
 lowerCamelCase__     :			List[str]     				=						list(transpose(_lowerCamelCase				)				)
 return scalar_multiply(_lowerCamelCase			,   1 / det				)






def        lowerCamelCase_  (						_lowerCamelCase				):
 return not isinstance(_lowerCamelCase			,   _lowerCamelCase				) and not isinstance(matrix[0]			,   _lowerCamelCase				)






def        lowerCamelCase_  (						_lowerCamelCase				):
 return len(_lowerCamelCase				), len(matrix[0]				)






def        lowerCamelCase_  (						_lowerCamelCase			,   _lowerCamelCase				):
 lowerCamelCase__     :			Tuple     				=						_shape(_lowerCamelCase				) + _shape(_lowerCamelCase				)
 if shape[0] != shape[3] or shape[1] != shape[2]:
  lowerCamelCase__     :			List[Any]     				=						(
      'operands could not be broadcast together with shape '
      f'''({shape[0], shape[1]}), ({shape[2], shape[3]})'''
  )
  raise ValueError(_lowerCamelCase				)
 return (shape[0], shape[2]), (shape[1], shape[3])






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


if __name__ == "__main__":
      import doctest

      doctest.testmod()
      main()









"""simple docstring"""
def        lowerCamelCase_  (						_lowerCamelCase				):
 lowerCamelCase__     :			int     				=						5381
 for x in s:
  lowerCamelCase__     :			Union[str, Any]     				=						((hash_value << 5) + hash_value) + ord(_lowerCamelCase				)
 return hash_value & 0Xffffffff

