# Transpose matrix

This tool calculates the transpose of a matrix.

## Transpose Matrix

The transpose of a matrix with n rows and p columns is a matrix with p rows and n columns in which rows and columns are exchanged. Thus, the columns of the transpose matrix of M are the rows of M matrix. For example,

`M = [[1,2],[-8,6],[0,7]]` then, the transpose of `M`, noted `M^T` or \({} ^t\! M\) is

`M^T = [[1,-8,0],[2,6,7]]`

Another example,

`M = [[5,2,4],[1,-7,3],[0,9,8]]` then,

`M^T = [[5,1,0],[2,-7,9],[4,3,8]]`

## See also

Adjoint matrix

Linear algebra Calculators