# Transpose of a Matrix

## Transpose of a Matrix

Matrix M$$^{\textrm{T}}$$ obtained by interchanging the rows and columns of a given matrix M such that each element $$a_{ij}$$ of M becomes the element $$a_{ji}$$ of M$$^{\textrm{T}}$$.

### Example

The transpose of matrix A below is matrix B.

A = $$\begin{pmatrix} –3 & 6 & 7\\4 & –8 & 5\end{pmatrix}$$

B = $$\begin{pmatrix} –3 & 4\\6 & –8\\7 & 5\end{pmatrix}$$

Therefore, the matrices A and B are compatible.