What Is the '@=' Symbol for in Python

What does the at (@) symbol do in Python?

An @ symbol at the beginning of a line is used for class and function decorators:

PEP 318: Decorators
Python Decorators

The most common Python decorators are:

@property
@classmethod
@staticmethod

An @ in the middle of a line is probably matrix multiplication:

@ as a binary operator.

What is the '@=' symbol for in Python?

From the documentation:

The @ (at) operator is intended to be used for matrix multiplication. No builtin Python types implement this operator.

The @ operator was introduced in Python 3.5. @= is matrix multiplication followed by assignment, as you would expect. They map to __matmul__, __rmatmul__ or __imatmul__ similar to how + and += map to __add__, __radd__ or __iadd__.

The operator and the rationale behind it are discussed in detail in PEP 465.

^=, -= and += symbols in Python

As almost any modern language, Python has assignment operators
so they can use them every time you want to assign a value to a variable after doing some arithmetic or logical operation, both (assignment and operation) are expressed in a compact way in one statement...

Table from Tutorials Point:

Operator Description Example
= Assigns values from right side operands to left side operand c = a + b assigns value of a + b into c
+= Add AND It adds right operand to the left operand and assign the result to left operand c += a is equivalent to c = c + a
-= Subtract AND It subtracts right operand from the left operand and assign the result to left operand c -= a is equivalent to c = c - a
*= Multiply AND It multiplies right operand with the left operand and assign the result to left operand c *= a is equivalent to c = c * a
/= Divide AND It divides left operand with the right operand and assign the result to left operand c /= a is equivalent to c = c / a
%= Modulus AND It takes modulus using two operands and assign the result to left operand c %= a is equivalent to c = c % a
**= Exponent AND Performs exponential (power) calculation on operators and assign value to the left operand c **= a is equivalent to c = c ** a
//= Floor Division It performs floor division on operators and assign value to the left operand c //= a is equivalent to c = c // a

What does the - (dash-greater-than arrow symbol) mean in a Python method signature?
This is function annotations. It can be use to attach additional information to the arguments or a return values of functions. It is a useful way to say how a function must be used.
Functions annotations are stored in a function's __annotations__ attribute.
Use Cases (From documentation)
Providing typing information
Type checking
Let IDEs show what types a function expects and returns
Function overloading / generic functions
Foreign-language bridges
Adaptation
Predicate logic functions
Database query mapping
RPC parameter marshaling
Other information
Documentation for parameters and return values
From python-3.5 it can be used for Type Hints

How to print symbols vertically in python?
def draw_symbol():
    for num in range(8):
        print("*")
    return
draw_symbol()
would result in:
*
*
*
*
*
*
*
*
What does the caret (^) operator do?
It's a bitwise XOR (exclusive OR).
It evaluates to True if and only if its arguments differ (one is True, the other is False).
To demonstrate:
>>> 0^0
0
>>> 1^1
0
>>> 1^0
1
>>> 0^1
1
To explain one of your own examples:
>>> 8^3
11
Think about it this way:
1000  # 8 (binary)
0011  # 3 (binary)
----  # APPLY XOR ('vertically')
1011  # result = 11 (binary)
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Operator	Description	Example
=	Assigns values from right side operands to left side operand	c = a + b assigns value of a + b into c
+= Add AND	It adds right operand to the left operand and assign the result to left operand	c += a is equivalent to c = c + a
-= Subtract AND	It subtracts right operand from the left operand and assign the result to left operand	c -= a is equivalent to c = c - a
*= Multiply AND	It multiplies right operand with the left operand and assign the result to left operand	c = a is equivalent to c = c a
/= Divide AND	It divides left operand with the right operand and assign the result to left operand	c /= a is equivalent to c = c / a
%= Modulus AND	It takes modulus using two operands and assign the result to left operand	c %= a is equivalent to c = c % a
**= Exponent AND	Performs exponential (power) calculation on operators and assign value to the left operand	c = a is equivalent to c = c a
//= Floor Division	It performs floor division on operators and assign value to the left operand	c //= a is equivalent to c = c // a