Rotating a matrix by 90 degrees clockwise is a common problem in computer science and technical interviews. This problem can be particularly interesting because the goal is to perform the rotation in place, without using additional memory for a new matrix. In this guide, we will explore how to achieve this with a clear explanation and example code.

## Problem Description

You are given an n x n 2D matrix `A`

representing an image. Your task is to rotate the image clockwise at 90 degrees in place. If you use an additional array, you will only receive partial credit.

### Problem Constraints

**1≤n≤1000**

### Input Format

**A 2D matrix A of integers**

### Output Format

`The 2D rotated matrix`

### Example Input

```
[
[1, 2],
[3, 4]
]
```

### Example Output

```
[
[3, 1],
[4, 2]
]
```

### Example Explanation

After rotating the matrix by 90 degrees:

- 1 goes to position 2
- 2 goes to position 4
- 4 goes to position 3
- 3 goes to position 1

#### Step-by-Step Solution

##### Step 1: Transpose the Matrix

Transposing a matrix means converting its rows into columns and columns into rows. This can be done by swapping elements across the main diagonal (top-left to bottom-right diagonal).

##### Step 2: Reverse Each Row

Once the matrix is transposed, the next step is to reverse each row. This will effectively rotate the matrix by 90 degrees clockwise.

### Example Code

Here’s a JavaScript function to perform the rotation:

```
function rotateMatrix(A) {
const n = A.length;
// Step 1: Transpose the matrix
for (let i = 0; i < n; i++) {
for (let j = i; j < n; j++) {
let temp = A[i][j];
A[i][j] = A[j][i];
A[j][i] = temp;
}
}
// Step 2: Reverse each row
for (let i = 0; i < n; i++) {
A[i].reverse();
}
return A;
}
// Example usage:
let matrix = [
[1, 2],
[3, 4]
];
console.log(rotateMatrix(matrix));
```

### Explanation of the Code

**Transpose the Matrix:**

- Loop through the matrix using two nested loops.
- Swap elements
`A[i][j]`

and`A[j][i]`

to transpose the matrix.

**Reverse Each Row:**

- Use the built-in
`reverse()`

method to reverse each row in the transposed matrix.

**Return the Rotated Matrix:**

- After transposing and reversing each row, the matrix is rotated by 90 degrees clockwise.

## Conclusion

Rotating a matrix in place is a valuable skill that showcases your understanding of array manipulation and in-place algorithms. By transposing the matrix and then reversing each row, you can achieve the desired rotation without using extra space. Practice this method to enhance your problem-solving abilities in technical interviews and coding challenges.