Matrix Row-Column Interchange

Easy

In linear algebra and matrix theory, one of the most essential operations is the row-column interchange of a matrix, commonly known as matrix transposition. This fundamental transformation reflects a matrix across its main diagonal, effectively swapping the row and column indices of every element. Given a matrix A of dimensions m × n (where m is the number of rows and n is the number of columns), the row-column interchange produces a new matrix A^T of dimensions n × m. The element at position (i, j) in the original matrix moves to position (j, i) in the resulting matrix: $$A^T_{ij} = A_{ji}$$ Geometric Interpretation: Visually, this operation can be understood as reflecting the matrix across its main diagonal (the line running from the top-left to the bottom-right). For a rectangular matrix, this also changes the shape—a wide matrix becomes tall, and vice versa. Key Properties: Applying the operation twice returns the original matrix: (A^T)^T = A The diagonal elements of a square matrix remain unchanged This operation preserves symmetry in symmetric matrices Your Task: Write a Python function that performs the row-column interchange on a given 2D matrix. The function should: Accept a 2D list representing a matrix with m rows and n columns Return a new 2D list representing the interchanged matrix with n rows and m columns Handle matrices of any valid dimensions (including single-row or single-column matrices)

Example 1

Input

matrix = [[1, 2, 3], [4, 5, 6]]

Output

[[1, 4], [2, 5], [3, 6]]

Explanation

The input is a 2×3 matrix (2 rows, 3 columns). After the row-column interchange: • The first row [1, 2, 3] becomes the first column • The second row [4, 5, 6] becomes the second column Element mapping: • matrix[0][0] = 1 → result[0][0] = 1 • matrix[0][1] = 2 → result[1][0] = 2 • matrix[0][2] = 3 → result[2][0] = 3 • matrix[1][0] = 4 → result[0][1] = 4 • matrix[1][1] = 5 → result[1][1] = 5 • matrix[1][2] = 6 → result[2][1] = 6 The resulting 3×2 matrix is [[1, 4], [2, 5], [3, 6]].

Example 2

Input

matrix = [[1, 2], [3, 4]]

Output

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

Explanation

This is a 2×2 square matrix. The row-column interchange swaps elements across the main diagonal: • Elements on the main diagonal (1 and 4) stay in place • matrix[0][1] = 2 swaps with matrix[1][0] = 3 The original matrix: The result: | 1 2 | | 1 3 | | 3 4 | → | 2 4 | Notice how the off-diagonal elements exchanged positions while diagonal elements remained fixed.

Example 3

Input

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

Output

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

Explanation

This is a 3×3 square matrix. The row-column interchange reflects elements across the main diagonal: • Diagonal elements (1, 5, 9) remain unchanged at positions (0,0), (1,1), (2,2) • Upper triangle elements move to lower triangle: 2→(1,0), 3→(2,0), 6→(2,1) • Lower triangle elements move to upper triangle: 4→(0,1), 7→(0,2), 8→(1,2) Original: Result: | 1 2 3 | | 1 4 7 | | 4 5 6 | → | 2 5 8 | | 7 8 9 | | 3 6 9 | This demonstrates the reflection across the main diagonal (from top-left to bottom-right).

Constraints

1 ≤ m ≤ 100 (number of rows in the input matrix)
1 ≤ n ≤ 100 (number of columns in the input matrix)
-10⁶ ≤ matrix[i][j] ≤ 10⁶ (element values)
The matrix will always have at least one element
All rows of the matrix will have the same length (valid rectangular matrix format)
Elements can be integers or floating-point numbers