<s>[INST] If $A$, $B$ are $3\times 3$ matrices, and all elements are different from each other and greater in their absolute value than 3, then is $AB \ne 0$? 
Let $A$ and $B$ be two $3\times 3$ matrices. All entries of $A$ are distinct and all entries of $B$ are distinct. All entries in both matrices are greater in their absolute value than 3. Then $AB \ne 0$.

Is this true or false, and why?
 [/INST] $$\begin{pmatrix}  4 & 8 & 12 \\ 5 & 10 & 15 \\ 7 & 14 & 21 \end{pmatrix} 
\begin{pmatrix}  -28 & -35 & -49 \\ 8 & 10 & 14 \\ 4 & 5 & 7 \end{pmatrix} 
=
\begin{pmatrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{pmatrix}$$
The idea was to start with
$$\begin{pmatrix}  1 & 2 & 3 \\ 1 & 2 & 3 \\ 1 & 2 & 3 \end{pmatrix} 
\begin{pmatrix}  -7 & -7 & -7 \\ 2 & 2 & 2 \\ 1 & 1 & 1 \end{pmatrix} $$
and then experiment multiplying rows and columns respectively by  constants  until the elements in each respective matrix is distinct. You can read of those constants from the first column and last row: $4, 5, 7$.
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