

from __future__ import annotations

from decimal import Decimal

from numpy import array





def 	__a     (      A__			:  list[list[float]]       ):
    SCREAMING_SNAKE_CASE										=   Decimal

    # Check if the provided matrix has 2 rows and 2 columns
    # since this implementation only works for 2x2 matrices
    if len(A__       ) == 2 and len(matrix[0]       ) == 2 and len(matrix[1]       ) == 2:
        # Calculate the determinant of the matrix
        SCREAMING_SNAKE_CASE										=   float(
            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
        SCREAMING_SNAKE_CASE										=   [[0.0, 0.0], [0.0, 0.0]]
        SCREAMING_SNAKE_CASE							,	SCREAMING_SNAKE_CASE										=   matrix[1][1], matrix[0][0]
        SCREAMING_SNAKE_CASE							,	SCREAMING_SNAKE_CASE										=   -matrix[1][0], -matrix[0][1]

        # Calculate the inverse of the matrix
        return [
            [(float(d(A__       )       ) / determinant) or 0.0 for n in row] for row in swapped_matrix
        ]
    elif (
        len(A__       ) == 3
        and len(matrix[0]       ) == 3
        and len(matrix[1]       ) == 3
        and len(matrix[2]       ) == 3
    ):
        # Calculate the determinant of the matrix using Sarrus rule
        SCREAMING_SNAKE_CASE										=   float(
            (
                (d(matrix[0][0]       ) * d(matrix[1][1]       ) * d(matrix[2][2]       ))
                + (d(matrix[0][1]       ) * d(matrix[1][2]       ) * d(matrix[2][0]       ))
                + (d(matrix[0][2]       ) * d(matrix[1][0]       ) * d(matrix[2][1]       ))
            )
            - (
                (d(matrix[0][2]       ) * d(matrix[1][1]       ) * d(matrix[2][0]       ))
                + (d(matrix[0][1]       ) * d(matrix[1][0]       ) * d(matrix[2][2]       ))
                + (d(matrix[0][0]       ) * d(matrix[1][2]       ) * d(matrix[2][1]       ))
            )       )
        if determinant == 0:
            raise ValueError("This matrix has no inverse."       )

        # Creating cofactor matrix
        SCREAMING_SNAKE_CASE										=   [
            [d(0.0       ), d(0.0       ), d(0.0       )],
            [d(0.0       ), d(0.0       ), d(0.0       )],
            [d(0.0       ), d(0.0       ), d(0.0       )],
        ]
        SCREAMING_SNAKE_CASE										=   (d(matrix[1][1]       ) * d(matrix[2][2]       )) - (
            d(matrix[1][2]       ) * d(matrix[2][1]       )
        )
        SCREAMING_SNAKE_CASE										=   -(
            (d(matrix[1][0]       ) * d(matrix[2][2]       )) - (d(matrix[1][2]       ) * d(matrix[2][0]       ))
        )
        SCREAMING_SNAKE_CASE										=   (d(matrix[1][0]       ) * d(matrix[2][1]       )) - (
            d(matrix[1][1]       ) * d(matrix[2][0]       )
        )
        SCREAMING_SNAKE_CASE										=   -(
            (d(matrix[0][1]       ) * d(matrix[2][2]       )) - (d(matrix[0][2]       ) * d(matrix[2][1]       ))
        )
        SCREAMING_SNAKE_CASE										=   (d(matrix[0][0]       ) * d(matrix[2][2]       )) - (
            d(matrix[0][2]       ) * d(matrix[2][0]       )
        )
        SCREAMING_SNAKE_CASE										=   -(
            (d(matrix[0][0]       ) * d(matrix[2][1]       )) - (d(matrix[0][1]       ) * d(matrix[2][0]       ))
        )
        SCREAMING_SNAKE_CASE										=   (d(matrix[0][1]       ) * d(matrix[1][2]       )) - (
            d(matrix[0][2]       ) * d(matrix[1][1]       )
        )
        SCREAMING_SNAKE_CASE										=   -(
            (d(matrix[0][0]       ) * d(matrix[1][2]       )) - (d(matrix[0][2]       ) * d(matrix[1][0]       ))
        )
        SCREAMING_SNAKE_CASE										=   (d(matrix[0][0]       ) * d(matrix[1][1]       )) - (
            d(matrix[0][1]       ) * d(matrix[1][0]       )
        )

        # Transpose the cofactor matrix (Adjoint matrix)
        SCREAMING_SNAKE_CASE										=   array(A__       )
        for i in range(3       ):
            for j in range(3       ):
                SCREAMING_SNAKE_CASE										=   cofactor_matrix[j][i]

        # Inverse of the matrix using the formula (1/determinant) * adjoint matrix
        SCREAMING_SNAKE_CASE										=   array(A__       )
        for i in range(3       ):
            for j in range(3       ):
                inverse_matrix[i][j] /= d(A__       )

        # Calculate the inverse of the matrix
        return [[float(d(A__       )       ) or 0.0 for n in row] for row in inverse_matrix]
    raise ValueError("Please provide a matrix of size 2x2 or 3x3."       )

'''simple docstring'''

def        UpperCAmelCase_ (  lowerCamelCase_			):







 """simple docstring"""


 lowerCAmelCase__     :   str     		=	len(lowerCamelCase_			)
 lowerCAmelCase__     :   Optional[Any]     		=	len(matrix[0]			)
 lowerCAmelCase__     :   Any     		=	min(lowerCamelCase_      ,			lowerCamelCase_			)

 for row in range(lowerCamelCase_			):
  # Check if diagonal element is not zero
  if matrix[row][row] != 0:
   # Eliminate all the elements below the diagonal
   for col in range(row + 1      ,			lowerCamelCase_			):
    lowerCAmelCase__     :   Tuple     		=	matrix[col][row] / matrix[row][row]
    for i in range(lowerCamelCase_      ,			lowerCamelCase_			):
     matrix[col][i] -= multiplier * matrix[row][i]
  else:
   # Find a non-zero diagonal element to swap rows
   lowerCAmelCase__     :   Dict     		=	True
   for i in range(row + 1      ,			lowerCamelCase_			):
    if matrix[i][row] != 0:
     lowerCAmelCase__		,     lowerCAmelCase__     :   Optional[Any]     		=	matrix[i], matrix[row]
     lowerCAmelCase__     :   Optional[Any]     		=	False
     break
   if reduce:
    rank -= 1
    for i in range(lowerCamelCase_			):
     lowerCAmelCase__     :   Union[str, Any]     		=	matrix[i][rank]

            # Reduce the row pointer by one to stay on the same row
   row -= 1

 return rank


if __name__ == "__main__":
     import doctest

     doctest.testmod()





