Calculate inverse matrix 2x2 and n dimension

 

Result in simulation python

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Source code 

# Function to calculate the transpose of a matrix

def calculate_transpose(matrix):

    # Determine the number of rows and columns in the matrix

    rows = len(matrix)

    columns = len(matrix[0])

    # Initialize the transposed matrix

    transposed_matrix = [[0] * rows for _ in range(columns)]

    # Iterate over the rows of the original matrix

    for i in range(rows):

        # Iterate over the columns of the original matrix

        for j in range(columns):

            # Assign the value from the original matrix to the transposed matrix

            transposed_matrix[j][i] = matrix[i][j]

    return transposed_matrix

# Function to calculate the determinant of a matrix

def calculate_determinant(matrix):

    # Base case for 2x2 matrix

    if len(matrix) == 2:

        determinant = matrix[0][0] * matrix[1][1] - matrix[0][1] * matrix[1][0]

        return determinant

    det = 0

    for c in range(len(matrix)):

        sign = (-1) ** c

        sub_matrix = [row[:c] + row[c+1:] for row in matrix[1:]]

        sub_det = calculate_determinant(sub_matrix)

        det += sign * matrix[0][c] * sub_det

    return det

# Function to calculate the matrix of minors

def calculate_matrix_of_minors(matrix):

    minors = []

    n = len(matrix)

    for i in range(n):

        row = []

        for j in range(n):

            submatrix = [row[:j] + row[j+1:] for row in (matrix[:i] + matrix[i+1:])]

            minor = calculate_determinant(submatrix)

            row.append(minor)

        minors.append(row)

    return minors

# Function to calculate the matrix of cofactors

def calculate_matrix_of_cofactors(matrix):

    cofactors = []

    n = len(matrix)

    for i in range(n):

        row = []

        for j in range(n):

            cofactor = (-1) ** (i + j) * matrix[i][j]

            row.append(cofactor)

        cofactors.append(row)

    return cofactors

# Function to calculate the inverse of an n x n matrix

def calculate_inverse(matrix):

    n = len(matrix)

    determinant = calculate_determinant(matrix)

    if determinant == 0:

        raise ValueError("The matrix has no inverse.")

    minors = calculate_matrix_of_minors(matrix)

    cofactors = calculate_matrix_of_cofactors(minors)

    adjugate = calculate_transpose(cofactors)

    inverse_matrix = [[adjugate[i][j] / determinant for j in range(n)] for i in range(n)]

    return inverse_matrix

# Function to display a matrix

def display(matrix):

    for row in matrix:

        print(" ".join(str(num) for num in row))

# Function to enter a matrix from user input

def enter_matrix():

    dimension = int(input("Enter the dimension of the matrix: "))

    matrix = []

    for i in range(dimension):

        row = []

        for j in range(dimension):

            while True:

                try:

                    element = int(input(f"Enter element at position a{i+1}{j+1}: "))

                    break

                except ValueError:

                    print("Invalid input. Please enter a numeric value.")

            row.append(element)

        matrix.append(row)

    return matrix

while True:

    try:

        matrix = enter_matrix()

        print("\nMatrix:")

        display(matrix)

        print("\nTranspose Matrix:")

        transpose_matrix = calculate_transpose(matrix)

        display(transpose_matrix)

        determinant = calculate_determinant(matrix)

        print("\nDeterminant:", determinant)

        print("\nInverse Matrix:")

        if len(matrix) >= 2:  

            inverse_matrix = calculate_inverse(matrix)

            display(inverse_matrix)

        else:

            print("Inverse calculation is supported only for matrices larger than or equal to 2x2.")

    except ValueError as e:

        print(str(e))