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.

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