Originally Posted by

**roninpro** In that case, I would like to draw your attention to an important property: no matter how you swap rows and columns, you preserve the numbers in a particular (labeled) row or column. Let me give you an example.

Consider the matrix

$\displaystyle

A=\begin{pmatrix}

15 & 2 & 1 & 12\\

4 & 9 & 10 & 7\\

8 & 5 & 6 & 11\\

3 & 14 & 13 & 0

\end{pmatrix}

$

The first column contains the numbers 15, 4, 8, 3. If I swap a few rows and columns, I might receive

$\displaystyle

A'=\begin{pmatrix}

9 & 4 & 10 & 7\\

14 & 3 & 13 & 0\\

5 & 8 & 6 & 11\\

2 & 15 & 1 & 12

\end{pmatrix}

$

Observe that I still have a column that contains 15, 4, 8, 3 - they are just permuted.

Can you see how to use this property to show that your matrices cannot be transformed into one another?