def Gauss_elimination(A):
    R = A.copy()             #Result
    m, n = len(R), len(R[0]) #Size of matrix
    row = col = 0

    while row < m:
        #Step 1: Determines the leftmost column that does not contain all zeroes
        while col < n and all(isZero(R[i][col]) for i in range(row, m)):
            col += 1

        if col == n: #Echelon matrix
            break
        
        #Step 2: Select the first line with a non-zero term. Switch two rows
        pivot_row = row + [not isZero(R[i][col]) for i in range(row, m)].index(True)
        switchRow(R, row, pivot_row)
        
        #Step 3: With the leading term from Step 2 being a≠0 , multiply the row containing it by 1/a
        mulRow(R, row, 1/R[row][col])
            
        #Step 4: Add an appropriate multiple of the top line to each bottom line to turn the terms below the leading number into 0
        for i in range(row + 1, m):
            multiplier = R[i][col] / R[row][col]
            addRow(R, i, row, -multiplier)
    
        #Step 5: Repeat the steps until you get the echolon matrix.
        row += 1

    printMatrix(R)
    print("\n")

    return R