Click For Counter Example

$\begin{pmatrix}\ 3 & 2 \\ 0 & 1\end{pmatrix}$ and $\begin{pmatrix}\ 4 & 9 \\ 2 & 3\end{pmatrix}$ are invertible matrices because each has a rank = 2

(1)
\begin{pmatrix} \ 3 & 2 \\ 0 & 1\end{pmatrix}\begin{pmatrix}\ 4 & 9 \\ 2 & 3\end{pmatrix}\ne \begin{pmatrix}\ 4 & 9 \\ 2 & 3\end{pmatrix}\begin{pmatrix}\ 3 & 2 \\ 0 & 1 \end{pmatrix}

because

(2)
\begin{pmatrix} \ 16 & 33 \\ 2 & 3\end{pmatrix}\ne\begin{pmatrix}\ 12 & 17 \\ 6 & 7 \end{pmatrix}
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