Added subsections when they appear, added all of the appendices, and finished the packet
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Let $A$, $B$, and $C$ be matrices such that $A(BC)$ is defined. Then $(AB)C$ is also defined and $A(BC)=(AB)C$; that is, matrix multiplication is associative.
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\end{theorem}
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\subsection*{Applications}
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\addcontentsline{toc}{subsection}{Applications}
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\begin{definition}
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\hfill\\
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An \textbf{incidence matrix} is a square matrix in which all the entries are either zero or one and, for convenience, all the diagonal entries are zero. If we have a relationship on a set of $n$ objects that we denote $1, 2, \dots, n$, then we define the associated incidence matrix $A$ by $A_{ij} = 1$ if $i$ is related to $j$, and $A_{ij} = 0$ otherwise.
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