# Ask different questions

Rather than assess whether my students can do matrix multiplication by having them multiply matrices without a calculator, I decided to ask a different question. After all, the point is about understanding and not computation, right? So, instead of giving them a non-calculator section on their quiz, I changed the question:

Given that
$\left[ \begin{array} {cc} 5 & 2\\ 7 & 3\end{array} \right] \left[ \begin{array} {cc} 1 & -4\\ -6 & 9\end{array} \right]= \left[ \begin{array} {cc} -7 & -2\\ -11 & -1\end{array} \right]$

explain the calculation that gives the entry in the first row, second column of the product matrix.