The transpose of a matrix A, denoted by A^T, may be constructed by any one of the following methods:

1. Write the rows of A as the columns of A^T;

2. Write the columns of A as the rows of A^T.

Formally, the i-th row, j-th column element of A^T is the j-th row, i-th column element of A:

A^T[j,i] = A[i, j]

If A is an m × n matrix, then A^T is an n × m matrix. For example,

If the given matrix is

1 2 3

4 5 6

7 8 9

The traspose matrix will be

1 4 7

2 5 8

3 6 9