Traspose of a matrix

Tranpose of a matrix A^T is obtained from A by changing its rows into columns and its columns into rows.
The first row of A is the first column of A^T.

Properties of Transpose

1. (A^T)^T = A
2. (A+B) ^T = A^T+B^T ( A and B must have the same order)
3. (kA) ^T = kA^T., (k is any scalar)
4. (AB) ^T = B^TA^T