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Q52Section C (Section C)52 of 60

Determinant via column operations

Consider the real matrices A=(a3d3b3e−2c3f1),B=(abc1−352d2e2f),C=(abcdef−1−49).A=\begin{pmatrix}a&3d&3\\b&3e&-2\\c&3f&1\end{pmatrix},\quad B=\begin{pmatrix}a&b&c\\1&-3&5\\2d&2e&2f\end{pmatrix},\quad C=\begin{pmatrix}a&b&c\\d&e&f\\-1&-4&9\end{pmatrix}. If the determinant of AA is −48-48 and the determinant of BB is 22, then the determinant of CC equals __________ (in integer)

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