# 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 $$A^t$$...