Matrix Rotation: A Must-Know for Devs & ML Engineers

🧠 Why Learn This?

Matrix rotation isn't just a coding interview favorite It's used in AI, ML, and image processing to manipulate data efficiently.

Think:

• Rotating images during training (data augmentation)
• Working with tensors in deep learning
• Optimizing spatial transformations with minimal memory

Mastering this helps you write cleaner, faster, and smarter code especially in AI-heavy projects. ✅

Rotate Image

You are given an n x n 2D matrix representing an image, rotate the image by 90 degrees (clockwise).

Want to rotate a 2D matrix 90° clockwise in-place without using extra space?

This classic interview problem teaches an elegant trick using matrix transposition + row reversal.

Let’s break it down step-by-step with visual examples so it actually sticks.

Original Matrix:

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

Rotated Matrix:

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

One way to solve it is:

1. Transposing
2. Reversing

What is Transposing a Matrix?

Transposing a matrix means flipping the matrix over its main diagonal, switching its rows with columns. Essentially, the element at position (i, j) in the original matrix moves to position (j, i) in the transposed matrix.

• Swap [0, 1] = 2, with [1, 0] = 4

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

• Swap [0, 2] = 3, with [2, 0] = 7

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

• Swap [1, 2] = 6, with [2 , 1] = 8

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

Final Transposed Matrix:

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

Step 2: Reverse Each Row

1. Reverse first row [1, 4, 7] → [7, 4, 1]
2. Reverse second row [2, 5, 8] → [8, 5, 2]
3. Reverse third row [3, 6, 9] → [9, 6, 3]

Final Reversed Matrix:

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

var rotate = function(matrix) {
    const n = matrix.length; 

    // Step 1: Transpose the matrix
    for (let i = 0; i < n; i++) {
        for (let j = i; j < n; j++) {
            // Swap matrix[i][j] with matrix[j][i]
   [matrix[i][j], matrix[j][i]] = [matrix[j][i], matrix[i][j]];
        }
    }  

    // Step 2: Reverse each row
    for (let i = 0; i < n; i++) {
        matrix[i].reverse();
    }
};

By first transposing the matrix (swap rows and columns) and then reversing each row, we get a clean 90° clockwise rotation — all done in-place with O(1) space.

Simple, elegant, and powerful.