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.