Transposed matrix

Let $A$ be a matrix, its transposed $A^t$ is obtained by swapping rows with columns. Let's see an example:

Consider matrix:

$$A=\left( \begin{array}{ccc} 5 & 1 & 2 \\ -3 & 0 & 1 \\ 4 & -5 & 2 \\ 1 & 0 & 4 \end{array} \right)$$

Its transpose will be:

$$A^t=\left( \begin{array}{cccc} 5 & -3 & 4 & 1 \\ 1 & 0 & -5 & 0 \\ 2 & 1 & 2 & 4 \end{array} \right)$$

The first column in matrix $A$ has become the first row in matrix $A^t$, the second column in matrix $A$ has become the second row in matrix $A^t$...