Transposed matrix

What is the transpose of the matrix $A=\left( \begin{array}{ccc} 1 & 8 & 1 \ 2 & 7 & 0 \ 0 & 5 & 3 \end{array} \right)$?

Let's swap rows with columns in order:

$$A^t=\left( \begin{array}{ccc} 1 & 2 & 0 \\ 8 & 7 & 5 \\ 1 & 0 & 3 \end{array} \right)$$

If $B^t=\left( \begin{array}{cccc} 1 & 3 & 5 & 6 \ 0 & 1 & 0 & 2 \ 0 & 5 & 4 & 1 \end{array} \right)$

calculate the original matrix $B$.

Now we just have to swap rows with columns again:

$$B=\left( \begin{array}{ccc} 1 & 0 & 0 \\ 3 & 1 & 5 \\ 5 & 0 & 4 \\ 6 & 2 & 1 \end{array} \right)$$

If we now calculate the transpose of this matrix we see that it is $B^t$.

$$B=\left( \begin{array}{ccc} 1 & 0 & 0 \\ 3 & 1 & 5 \\ 5 & 0 & 4 \\ 6 & 2 & 1 \end{array} \right)$$