# Import NumPy
import numpy as np

# Create two 2x2 matrices
A = np.array([[1, 2],
              [3, 4]])

B = np.array([[5, 6],
              [7, 8]])

# Matrix addition
S = A + B
print("Sum:\n", S)

# Matrix subtraction
D = A - B
print("Difference:\n", D)

# Element-wise multiplication (warning: not usually what you want)
E = A * B
print("Element-wise multiplication:\n", E)

# Matrix multiplication 
P = A @ B
print("Matrix multiplication:\n", P)

# Transpose of a matrix
G = A.T
print("Transpose:\n", G)

# Determinant of a matrix
det_A = np.linalg.det(A)
print("Determinant:\n", det_A)

# Inverse of a matrix
inv_A = np.linalg.inv(A)
print("Inverse:\n", inv_A)

#Solve a linear system
b = np.array([1, 4])  # Define the right-hand side vector
x = np.linalg.solve(A, b)  # Solve for x
print("Solution to Ax = b:\n", x)