## The challenge

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:**

Giveninput matrix= [ [1,2,3], [4,5,6], [7,8,9] ], rotate the input matrixin-placesuch that it becomes: [ [7,4,1], [8,5,2], [9,6,3] ]

**Example 2:**

Giveninput matrix= [ [ 5, 1, 9,11], [ 2, 4, 8,10], [13, 3, 6, 7], [15,14,12,16] ], rotate the input matrixin-placesuch that it becomes: [ [15,13, 2, 5], [14, 3, 4, 1], [12, 6, 8, 9], [16, 7,10,11] ]

## The first solution

With this solution, we loop through each column and row and swap the elements, then finally we loop through each row one last time and reverse them.

```
def rotate(self, matrix: List[List[int]]) -> None:
# Transpose the matrix
for i in range(len(matrix)):
for j in range(i, len(matrix)):
matrix[i][j], matrix[j][i] = matrix[j][i], matrix[i][j]
# Reverse each row
for i in range(len(matrix)):
matrix[i].reverse()
```

## An alternative solution

With this solution, we start by reversing the list and then loop through each column and row. Within this second loop, we swap the elements.

```
def rotate(self, matrix: List[List[int]]) -> None:
n = len(matrix)
matrix.reverse()
for x in range(n):
for y in range(n-1, x-1, -1):
matrix[x][y], matrix[y][x] = matrix[y][x], matrix[x][y]
```