# Transpose Matrix Calculator

Matrix is a grid function that has an ordered rectangular array of numbers. The numbers present in the array are called the entities. The numbers are arranged in rows and columns. The horizontal arrangement is called rows and the vertical arrangement of numbers is called columns.

## What is Transpose Matrix Calculator?

'**Transpose Matrix Calculator**' is an online tool that helps to calculate the transpose of a given matrix. Online Transpose Matrix Calculator helps you to calculate the transpose of a given matrix in a few seconds.

### Transpose Matrix Calculator

## How to Use the Transpose Matrix Calculator?

Please follow the steps below on how to use the calculator:

**Step 1:**Choose a drop-down list to find the transpose for 2 × 2 and 3 × 3 matrices.**Step 1:**Enter the numbers in the given input boxes.**Step 2:**Click on the**"Calculate"**button to find the transpose of a given matrix.**Step 3:**Click on the**"Reset"**button to clear the fields and find the transpose for different matrix values.

## How to Find Transpose of the Matrix?

**Matrix **is a mathematical function to represent a set of data usually a matrix used is a 2D matrix. To find the transpose of a matrix, we interchange the rows and columns of a given matrix. If A is the given matrix then the transpose of the matrix is represented by A^{T}.

\(A = \begin{matrix} a & b \\ c & d \end{matrix} \), then the \(A^T = \begin{matrix} a & c \\ b & d \end{matrix} \)

**Solved Examples on Transpose Matrix Calculator**

**Example 1:**

Find transpose of the given matrix A = \( \begin{bmatrix} 1 & 5 & 6 \\ 2 & 3 & 4 \\ 7 & 9 & 8 \end{bmatrix} \)

**Solution:**

Given: A = \( \begin{bmatrix} 1 & 5 & 6 \\ 2 & 3 & 4 \\ 7 & 9 & 8 \end{bmatrix} \)

A^{T} = \( \begin{bmatrix} 1 & 2 & 7 \\ 5 & 3 & 9 \\ 6 & 4 & 8 \end{bmatrix} \)

**Example 2:**

Find transpose of the given matrix A = \( \begin{bmatrix} 1 & 3 & 4 \\ 5 & 7 & 8 \\ 1 & 3 & 4 \end{bmatrix} \)

**Solution:**

Given: A = \( \begin{bmatrix} 1 & 3 & 4 \\ 5 & 7 & 8 \\ 1 & 3 & 4 \end{bmatrix} \)

A^{T} = \( \begin{bmatrix} 1 & 5 & 1 \\ 3 & 7 & 3 \\ 4 & 8 & 4 \end{bmatrix} \)

Similarly, you can use the calculator to find the transpose of given matrices:

- \( \begin{bmatrix} 2 & -1 & 3 \\ 4 & -5 & 1 \\ 1 & 6 & 7 \end{bmatrix} \)
- \( \begin{bmatrix} -4 &2 \\ -3 & 4 \end{bmatrix} \)

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