You are given an *n* x *n* 2D matrix representing an image.

Rotate the image by 90 degrees (clockwise).

**Note**:

You have to rotate the image **in-place**, which means you have to modify the input 2D matrix directly. **DO NOT** allocate another 2D matrix and do the rotation.

**Example 1**:

Input:[ [1,2,3], [4,5,6], [7,8,9] ]

Output:[ [7,4,1], [8,5,2], [9,6,3] ]

**Example 1**:

Input:[ [ 5, 1, 9,11], [ 2, 4, 8,10], [13, 3, 6, 7], [15,14,12,16] ]

Output:[ [15,13, 2, 5], [14, 3, 4, 1], [12, 6, 8, 9], [16, 7,10,11] ]

## Solution

```
from typing import List
class Solution:
def rotate(self, matrix: List[List[int]]) -> None:
n = len(matrix[0])
# transpose matrix
for i in range(n):
for j in range(i, n):
matrix[j][i], matrix[i][j] = matrix[i][j], matrix[j][i]
# reverse each row
for i in range(n):
matrix[i].reverse()
```

## Test Cases

```
test = Solution()
matrix = [
[1,2,3],
[4,5,6],
[7,8,9]
]
test.rotate(matrix)
assert matrix == [
[7,4,1],
[8,5,2],
[9,6,3]
]
print('All Passed!')
```

## Big O Analysis

**Space Complexity**: O(1)

**Time Complexity**: O(N^{2})