This C# program demonstrates how to calculate the transpose of a matrix. The transpose of a matrix is a new matrix in which the rows of the original matrix become the columns, and the columns become the rows. Transposition is a fundamental operation in linear algebra and matrix manipulation, often used in various scientific and engineering applications.

## Problem Statement

Write a C# program to find the transpose of a given matrix. Your program should take an input matrix, perform the transpose operation, and display the resulting transposed matrix.

## C# Program to Find Transpose of a Matrix

using System; class MatrixTranspose { static void Main() { int[,] matrix = { {1, 2, 3}, {4, 5, 6}, {7, 8, 9} }; int rows = matrix.GetLength(0); int cols = matrix.GetLength(1); int[,] transpose = new int[cols, rows]; // Finding the transpose of the matrix for (int i = 0; i < rows; i++) { for (int j = 0; j < cols; j++) { transpose[j, i] = matrix[i, j]; } } // Displaying the original matrix Console.WriteLine("Original Matrix:"); DisplayMatrix(matrix); // Displaying the transpose matrix Console.WriteLine("Transpose Matrix:"); DisplayMatrix(transpose); } static void DisplayMatrix(int[,] matrix) { int rows = matrix.GetLength(0); int cols = matrix.GetLength(1); for (int i = 0; i < rows; i++) { for (int j = 0; j < cols; j++) { Console.Write(matrix[i, j] + " "); } Console.WriteLine(); } } }

## How it Works

**Original Matrix:**Start with the original matrix that you want to transpose. Letâ€™s call this matrix A.**Create a New Matrix:**Create a new matrix, which will be the transpose of the original matrix. Initialize this new matrix with the appropriate dimensions, which are the reverse of the original matrixâ€™s dimensions. In other words, if the original matrix A is m x n, the new matrix A^T will be n x m.**Transpose Elements:**Now, go through each element of the original matrix A and copy it to the new matrix A^T, but swap the row and column indices. That is, the element at position (i, j) in matrix A becomes the element at position (j, i) in matrix A^T.You continue this process for all elements in the original matrix, copying them to their corresponding positions in the transposed matrix.**Result:**After completing the above steps, youâ€™ll have the transposed matrix A^T, where the rows of the original matrix A have become the columns of A^T, and the columns of A have become the rows of A^T.