Magic Square Check

A **magic square** is a square matrix in which the sum of every row, column, and both main diagonals is the same. Write a function `is_magic_square(matrix)` that determines whether a given square matrix is a magic square.

#### Function Signature
```python [main.nopy]
def is_magic_square(matrix: list[list[int]]) -> bool:
    pass
```

#### Input
- `matrix`: A list of lists of integers representing a square matrix (n x n).

#### Output
- Returns `True` if the matrix is a magic square, otherwise `False`.

#### Example Usage
```python [main.nopy]
is_magic_square([[2, 7, 6], [9, 5, 1], [4, 3, 8]])  # True
is_magic_square([[1, 2], [3, 4]])  # False
is_magic_square([[16, 2, 3, 13], [5, 11, 10, 8], [9, 7, 6, 12], [4, 14, 15, 1]])  # True
```

#### Constraints
- The input matrix will always be square (n x n).
- The matrix will contain only integers.