a = [[1, 2], [3, 4]]
b = [[5, 6], [7, 8]]

c = [[0, 0], [0, 0]]
for i in range(len(a)):
    for j in range(len(b[0])):
        for k in range(len(b)):
            c[i][j] += a[i][k] * b[k][j]

print(c)

import numpy as np
a = np.array([[1, 2], [3, 4]])
b = np.array([[5, 6], [7, 8]])
c = np.dot(a, b)
print(c)

import numpy as np
a = np.array([[1, 2], [3, 4]])
b = np.linalg.inv(a)
print(b)

import numpy as np
a = np.array([[1, 2], [3, 4]])
b = np.linalg.det(a)
print(b)

import numpy as np
a = np.array([[1, 2], [3, 4]])
b = np.transpose(a)
print(b)

import numpy as np
a = np.array([[1, 2], [3, 4]])
b = np.array([1, 2])
x = np.linalg.solve(a, b)
print(x)