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Math 192r, Problem Set \#15 \\
(due 11/15/01)
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\begin{enumerate}
\item
Using the combinatorial definition of the determinant,
prove that for all $n$-by-$n$ matrices $A,B$,
$\det(AB)=\det(A) \det(B)$.
\item
Use Lindstrom's lemma,
the interpretation of domino tilings as routings,
and a computer,
in order to count the domino tilings of an 8-by-8 square,
as well as the domino tilings of an 8-by-8 square
from which two (non-opposite) corners have been removed.
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