Transposed matrix

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

Example

Consider matrix:

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

Its transpose will be:

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

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 $A^{t}$ ...