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# Transpose Matrix Calculator

To use Transpose Matrix Calculator, select the order of matrix, enter the values, and hit calculate button

Table of Contents:

## Matrix Transpose Calculator

Matrix Transpose Calculator is used to perform a matrix operation which is known as transposition. Transposition is a process in which swapping the rows and columns of a matrix and gives the result in a new matrix where the columns and rows are interchanged.

## What is Matrix Transpose?

Transpose of the matrix is a process in which interchange the rows into columns or (columns into the rows) of the given matrix. In other words, if the order of any matrix “A” is “m x n” after processing it becomes “n x m” that is the order of the Transpose Matrix of “A”.

## Transpose Matrix Formula:

The Transpose matrix is denoted by “A^{t}” which is read as the transpose of the matrix “A”. The matrix “A^{t}” is obtained simply by changing the i^{th} element of the rows into the j^{th} element of the column. The general Formula of the Transpose Matrix is defined as.

If A = [a_{ij}] is a matrix with “m x n” order. Where “i” denotes the i^{th} rows and “j” denotes the j^{th} columns.

Then A^{t} = [a_{ji}] with the order “n x m” order. Where “j” denotes the j^{th} rows and “i” denotes the i^{th} columns after taking the transpose of the matrix.

## Examples

**Example 1:**

Find the transpose matrix of the matrix.

[4 -3 1]

[2 -3 4]

[3 -5 6]

**Solution:**

**Step 1: **Let the given matrix be equal to “A”.

A = [4 -3 1]

[2 -3 4]

[3 -5 6]

**Step 2:** The transpose matrix by swapping the rows into columns.

A^{t} = [4 -3 1]^{t}

[2 -3 4]

[3 -5 6]

A^{t} = [4 2 3]

[-3 -3 5]

[1 4 6]

**Example 2:**

Find the Transpose Matrix of the below matrix.

A = [1 -4 2]

[5 -3 0]

**Solution:**

The transpose of the matrix is get by swapping the rows into columns.

A^{t} = [1 -4 2]^{t}

[5 -3 0]

A^{t} = [1 5]

[-4 -3]

[2 0]