# Transpose of matrix

## The step-by-step process for calculating the transpose of a matrix:

- Write down the original matrix. Let’s call it A.
**Identify the number of rows and columns in the matrix A. Let’s call the number of rows m and the number of columns n.****Create a new matrix, called the transpose of A. This matrix will have n rows and m columns.****Copy the elements of the original matrix A to the new matrix in such a way that the rows of the original matrix become the columns of the****new matrix and the columns of the original matrix become the rows of the new matrix. That is, the element in the i-th row and j-th column of the original matrix should be placed in the j-th row and i-th column of the new matrix.**- The resulting matrix is the transpose of the original matrix.

**For example, suppose we have the following matrix A:**

A = [ [1, 2, 3],

[4, 5, 6]

]

**To find the transpose of this matrix, we follow the steps:**

Write down the original matrix A:

A = [ [1, 2, 3],

[4, 5, 6]

]

Identify the number of rows and columns in A:

m = 2, n = 3

Create a new matrix with swapped dimensions:

transpose = [

[0, 0],

[0, 0],

[0, 0]

]

Copy the elements of the original matrix to the new matrix in such a way that the rows of the original matrix become the columns of the new matrix and the columns of the original matrix become the rows of the new matrix:

transpose = [

[1, 4],

[2, 5],

[3, 6]

]

The resulting matrix is the transpose of the original matrix:

transpose of A = [ [1, 4],

[2, 5],

[3, 6]

]

So the transpose of the matrix A is [[1, 4], [2, 5], [3, 6]].