[Python] Matrix determinant

I have this function to get the determinant of a matrix:

def determinant(self) -> int:
"""
Calculates the Determinant of matrix objects.
Parameters
----------
self
Returns
-------
int
Example
-------
>>> _matrix = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]
>>> _matrix = Matrix(_matrix)
>>> _matrix.determinant()
0
"""
if self.row != self.column:
raise ValueError('Cannot get determinant of this matrix! Must be a square Matrix')
else:
def det(matrix):
row = len(matrix)
col = len(matrix[0])

if (row, col) == (1, 1):
return matrix[0][0]

# hard coding for 2x2
elif (row, col) == (2, 2):
return matrix[0][0] * matrix[1][1] - matrix[0][1] * matrix[1][0]

# using sarrus method to solve for 3x3, it's a little faster.
elif (row, col) == (3, 3):
matrix1 = matrix[:]

# Extending matrix to use Sarrus Rule.
for i in range(row - 1):
_col = []
for j in range(col):
_col.append(matrix1[j])
matrix1.append(_col)

# Calculating Determinant
# Adding part
add_pointers = [(i, i) for i in range(row)]
result = 0
for pointer in range(row):
temp = 1
for tup in add_pointers:
i, j = tup
temp *= matrix1[i + pointer][j]
result += temp

# Subtracting part
sub_pointers = [((row - 1) - i, 0 + i) for i in range(row)]
for pointers in range(row):
temp = 1
for tup in sub_pointers:
i, j = tup
temp *= matrix1[i + pointers][j]
result -= temp
return result

else:
sign = -1
result = 0
row1 = [matrix[0] * (sign ** i) for i in range(col)]
for x, y in enumerate(row1):
mat = matrix[:][1:]
sub_matrix = [[mat[j] for j in range(col) if j != x] for i in range(row - 1)]
result += y * det(sub_matrix)
return result

return det(self.matrix)


I have hard-coded the determinant of a 2x2 and 3x3 matrix, then I'm recusing through the rest for an nxn matrix.

This is extremely slow. What would be a faster method implemented in pure Python?

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