# 1. Introduction

Transposing a matrix involves converting rows into columns and vice versa. This is a common operation in linear algebra and is used in various fields such as physics, computer graphics, and statistics. In this tutorial, we will write a Java program to find the transpose of a given matrix.

# 2. Program Steps

1. Define a class named *MatrixTranspose*.

2. Inside the *main* method, define a 2D array *matrix* representing the matrix to be transposed.

3. Define a 2D array *transpose* to store the transposed matrix.

4. Use nested *for* loops to transpose the *matrix* by swapping its row and column indices and store the result in *transpose*.

5. Print the original *matrix* and its *transpose*.

# 3. Code Program

```
public class MatrixTranspose { // Step 1: Define a class named MatrixTranspose
public static void main(String[] args) { // Main method
// Step 2: Define a 2D array matrix representing the matrix to be transposed
int[][] matrix = {
{1, 2, 3},
{4, 5, 6},
{7, 8, 9}
};
// Step 3: Define a 2D array transpose to store the transposed matrix
int rows = matrix.length;
int columns = matrix[0].length;
int[][] transpose = new int[columns][rows];
// Step 4: Use nested for loops to transpose the matrix
for (int i = 0; i < rows; i++) {
for (int j = 0; j < columns; j++) {
transpose[j][i] = matrix[i][j];
}
}
// Step 5: Print the original matrix and its transpose
System.out.println("Original Matrix:");
for (int i = 0; i < rows; i++) {
for (int j = 0; j < columns; j++) {
System.out.print(matrix[i][j] + " ");
}
System.out.println();
}
System.out.println("Transposed Matrix:");
for (int i = 0; i < columns; i++) {
for (int j = 0; j < rows; j++) {
System.out.print(transpose[i][j] + " ");
}
System.out.println();
}
}
}
```

### Output:

Original Matrix: 1 2 3 4 5 6 7 8 9 Transposed Matrix: 1 4 7 2 5 8 3 6 9

# 4. Step By Step Explanation

– *Step 1:* A class named *MatrixTranspose* is defined.

– *Step 2:* A 2D array *matrix* representing the matrix to be transposed is defined inside the *main* method.

– *Step 3:* A 2D array *transpose* is defined to store the result of the transposed matrix.

– *Step 4:* Nested *for* loops are used to transpose the *matrix* by swapping its row and column indices and store the result in *transpose*.

– *Step 5:* The program prints the original *matrix* and its *transpose*.