Challenge: Create a 3x3 matrix of letters (NO REPEATS) such that the determinant of the matrix forms words from the 'multiplications'. For example, in a simple 2x2 case, take the matrix
$\begin{bmatrix}O & I\\N & R\end{bmatrix}$
the determinant of which is OR-IN. This forms 2 2-letter words. In the case of a 3x3, you will end up with 6 3-letter words if done correctly.
Don't know how to find the determinant of a matrix? Fear not, here's the guide (or read a more detailed explanation here):
$|A| = \begin{vmatrix} a & b & c\\d & e & f\\g & h & i \end{vmatrix} = a\begin{vmatrix} e & f\\h & i \end{vmatrix} - b\begin{vmatrix} d & f\\g & i \end{vmatrix} + c\begin{vmatrix} d & e\\g & h \end{vmatrix} = aei+bfg+cdh-ceg-bdi-afh . $
If that looks too complicated, here's another method that some find easier.
Don't worry about the additions and subtractions, I'm only concerned with the words formed. That said, if your words could be added and subtracted as base 26 numbers according to the determinant and result in a valid word, I would be incredibly impressed (a 100 reputation impressed, even). (This is mathematically impossible, determinant is always 0; sorry to get your hopes up). As usual, words are considered valid iff they are English words found on dictionary.com (read: this does not include (pre/suf)fixes, abbreviations, acronyms, etc.)
Answer
Try
$\begin{bmatrix} B & S & L\\I & A & U\\M & D & T \end{bmatrix}$
This produces the following words:
BAT
SUM
LID
LAM
BUD
SIT
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