#### Matrix Class

```# An OOP approach to representing and manipulating matrices

from __future__ import annotations

class Matrix:
"""
Matrix object generated from a 2D array where each element is an array representing
a row.
Rows can contain type int or float.
Common operations and information available.
>>> rows = [
...     [1, 2, 3],
...     [4, 5, 6],
...     [7, 8, 9]
... ]
>>> matrix = Matrix(rows)
>>> print(matrix)
[[1. 2. 3.]
[4. 5. 6.]
[7. 8. 9.]]

Matrix rows and columns are available as 2D arrays
>>> matrix.rows
[[1, 2, 3], [4, 5, 6], [7, 8, 9]]
>>> matrix.columns()
[[1, 4, 7], [2, 5, 8], [3, 6, 9]]

Order is returned as a tuple
>>> matrix.order
(3, 3)

Squareness and invertability are represented as bool
>>> matrix.is_square
True
>>> matrix.is_invertable()
False

Identity, Minors, Cofactors and Adjugate are returned as Matrices.  Inverse can be
a Matrix or Nonetype
>>> print(matrix.identity())
[[1. 0. 0.]
[0. 1. 0.]
[0. 0. 1.]]
>>> print(matrix.minors())
[[-3. -6. -3.]
[-6. -12. -6.]
[-3. -6. -3.]]
>>> print(matrix.cofactors())
[[-3. 6. -3.]
[6. -12. 6.]
[-3. 6. -3.]]
>>>  # won't be apparent due to the nature of the cofactor matrix
[[-3. 6. -3.]
[6. -12. 6.]
[-3. 6. -3.]]
>>> matrix.inverse()
Traceback (most recent call last):
...
TypeError: Only matrices with a non-zero determinant have an inverse

Determinant is an int, float, or Nonetype
>>> matrix.determinant()
0

Negation, scalar multiplication, addition, subtraction, multiplication and
exponentiation are available and all return a Matrix
>>> print(-matrix)
[[-1. -2. -3.]
[-4. -5. -6.]
[-7. -8. -9.]]
>>> matrix2 = matrix * 3
>>> print(matrix2)
[[3. 6. 9.]
[12. 15. 18.]
[21. 24. 27.]]
>>> print(matrix + matrix2)
[[4. 8. 12.]
[16. 20. 24.]
[28. 32. 36.]]
>>> print(matrix - matrix2)
[[-2. -4. -6.]
[-8. -10. -12.]
[-14. -16. -18.]]
>>> print(matrix ** 3)
[[468. 576. 684.]
[1062. 1305. 1548.]
[1656. 2034. 2412.]]

Matrices can also be modified
>>> print(matrix)
[[1. 2. 3.]
[4. 5. 6.]
[7. 8. 9.]
[10. 11. 12.]]
>>> print(matrix2)
[[3. 6. 9. 8.]
[12. 15. 18. 16.]
[21. 24. 27. 32.]]
>>> print(matrix *  matrix2)
[[90. 108. 126. 136.]
[198. 243. 288. 304.]
[306. 378. 450. 472.]
[414. 513. 612. 640.]]
"""

def __init__(self, rows: list[list[int]]):
error = TypeError(
"Matrices must be formed from a list of zero or more lists containing at "
"least one and the same number of values, each of which must be of type "
"int or float."
)
if len(rows) != 0:
cols = len(rows[0])
if cols == 0:
raise error
for row in rows:
if len(row) != cols:
raise error
for value in row:
if not isinstance(value, (int, float)):
raise error
self.rows = rows
else:
self.rows = []

# MATRIX INFORMATION
def columns(self) -> list[list[int]]:
return [[row[i] for row in self.rows] for i in range(len(self.rows[0]))]

@property
def num_rows(self) -> int:
return len(self.rows)

@property
def num_columns(self) -> int:
return len(self.rows[0])

@property
def order(self) -> tuple[int, int]:
return (self.num_rows, self.num_columns)

@property
def is_square(self) -> bool:
return self.order[0] == self.order[1]

def identity(self) -> Matrix:
values = [
[0 if column_num != row_num else 1 for column_num in range(self.num_rows)]
for row_num in range(self.num_rows)
]
return Matrix(values)

def determinant(self) -> int:
if not self.is_square:
return 0
if self.order == (0, 0):
return 1
if self.order == (1, 1):
return int(self.rows[0][0])
if self.order == (2, 2):
return int(
(self.rows[0][0] * self.rows[1][1])
- (self.rows[0][1] * self.rows[1][0])
)
else:
return sum(
self.rows[0][column] * self.cofactors().rows[0][column]
for column in range(self.num_columns)
)

def is_invertable(self) -> bool:
return bool(self.determinant())

def get_minor(self, row: int, column: int) -> int:
values = [
[
self.rows[other_row][other_column]
for other_column in range(self.num_columns)
if other_column != column
]
for other_row in range(self.num_rows)
if other_row != row
]
return Matrix(values).determinant()

def get_cofactor(self, row: int, column: int) -> int:
if (row + column) % 2 == 0:
return self.get_minor(row, column)
return -1 * self.get_minor(row, column)

def minors(self) -> Matrix:
return Matrix(
[
[self.get_minor(row, column) for column in range(self.num_columns)]
for row in range(self.num_rows)
]
)

def cofactors(self) -> Matrix:
return Matrix(
[
[
self.minors().rows[row][column]
if (row + column) % 2 == 0
else self.minors().rows[row][column] * -1
for column in range(self.minors().num_columns)
]
for row in range(self.minors().num_rows)
]
)

values = [
[self.cofactors().rows[column][row] for column in range(self.num_columns)]
for row in range(self.num_rows)
]
return Matrix(values)

def inverse(self) -> Matrix:
determinant = self.determinant()
if not determinant:
raise TypeError("Only matrices with a non-zero determinant have an inverse")
return self.adjugate() * (1 / determinant)

def __repr__(self) -> str:
return str(self.rows)

def __str__(self) -> str:
if self.num_rows == 0:
return "[]"
if self.num_rows == 1:
return "[[" + ". ".join(str(self.rows[0])) + "]]"
return (
"["
+ "\n ".join(
[
"[" + ". ".join([str(value) for value in row]) + ".]"
for row in self.rows
]
)
+ "]"
)

# MATRIX MANIPULATION
def add_row(self, row: list[int], position: int | None = None) -> None:
type_error = TypeError("Row must be a list containing all ints and/or floats")
if not isinstance(row, list):
raise type_error
for value in row:
if not isinstance(value, (int, float)):
raise type_error
if len(row) != self.num_columns:
raise ValueError(
"Row must be equal in length to the other rows in the matrix"
)
if position is None:
self.rows.append(row)
else:
self.rows = self.rows[0:position] + [row] + self.rows[position:]

def add_column(self, column: list[int], position: int | None = None) -> None:
type_error = TypeError(
"Column must be a list containing all ints and/or floats"
)
if not isinstance(column, list):
raise type_error
for value in column:
if not isinstance(value, (int, float)):
raise type_error
if len(column) != self.num_rows:
raise ValueError(
"Column must be equal in length to the other columns in the matrix"
)
if position is None:
self.rows = [self.rows[i] + [column[i]] for i in range(self.num_rows)]
else:
self.rows = [
self.rows[i][0:position] + [column[i]] + self.rows[i][position:]
for i in range(self.num_rows)
]

# MATRIX OPERATIONS
def __eq__(self, other: object) -> bool:
if not isinstance(other, Matrix):
return NotImplemented
return self.rows == other.rows

def __ne__(self, other: object) -> bool:
return not self == other

def __neg__(self) -> Matrix:
return self * -1

def __add__(self, other: Matrix) -> Matrix:
if self.order != other.order:
raise ValueError("Addition requires matrices of the same order")
return Matrix(
[
[self.rows[i][j] + other.rows[i][j] for j in range(self.num_columns)]
for i in range(self.num_rows)
]
)

def __sub__(self, other: Matrix) -> Matrix:
if self.order != other.order:
raise ValueError("Subtraction requires matrices of the same order")
return Matrix(
[
[self.rows[i][j] - other.rows[i][j] for j in range(self.num_columns)]
for i in range(self.num_rows)
]
)

def __mul__(self, other: Matrix | int | float) -> Matrix:
if isinstance(other, (int, float)):
return Matrix(
[[int(element * other) for element in row] for row in self.rows]
)
elif isinstance(other, Matrix):
if self.num_columns != other.num_rows:
raise ValueError(
"The number of columns in the first matrix must "
"be equal to the number of rows in the second"
)
return Matrix(
[
[Matrix.dot_product(row, column) for column in other.columns()]
for row in self.rows
]
)
else:
raise TypeError(
"A Matrix can only be multiplied by an int, float, or another matrix"
)

def __pow__(self, other: int) -> Matrix:
if not isinstance(other, int):
raise TypeError("A Matrix can only be raised to the power of an int")
if not self.is_square:
raise ValueError("Only square matrices can be raised to a power")
if other == 0:
return self.identity()
if other < 0:
if self.is_invertable():
return self.inverse() ** (-other)
raise ValueError(
"Only invertable matrices can be raised to a negative power"
)
result = self
for _ in range(other - 1):
result *= self
return result

@classmethod
def dot_product(cls, row: list[int], column: list[int]) -> int:
return sum(row[i] * column[i] for i in range(len(row)))

if __name__ == "__main__":
import doctest

doctest.testmod()
```