
<ol>
<li>Consider the two matrices below, and suppose you already have computed $\detname{A}=-120$.  What is $\detname{B}$?  Why?
\begin{align*}
A&amp;=
\begin{bmatrix}
 0 &amp; 8 &amp; 3 &amp; -4 \\
 -1 &amp; 2 &amp; -2 &amp; 5 \\
 -2 &amp; 8 &amp; 4 &amp; 3 \\
 0 &amp; -4 &amp; 2 &amp; -3
\end{bmatrix}
&amp;
B&amp;=
\begin{bmatrix}
 0 &amp; 8 &amp; 3 &amp; -4 \\
 0 &amp; -4 &amp; 2 &amp; -3 \\
 -2 &amp; 8 &amp; 4 &amp; 3 \\
 -1 &amp; 2 &amp; -2 &amp; 5
\end{bmatrix}
\end{align*}

</li>
<li>State the theorem that allows us to make yet another extension to our NMEx series of theorems.
</li>
<li>What is amazing about the interaction between matrix multiplication and the determinant?
</li>
</ol>