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Prove without expanding

1. | l m n | | y m q |

| x y z | = | x l p |

|p q r | | z n r |

(l is L)

$| \begin{matrix} l & m & n \\ x & y & z \\ p & q & r \end{matrix} | = | \begin{matrix} l & x & p \\ m & y & q \\ n & z & r \end{matrix} | (t a k i n g t r a n s p o s e) = - | \begin{matrix} x & l & p \\ y & m & q \\ z & n & r \end{matrix} | (int e r c h a n g i n g C_{1} a n d C_{2}) = | \begin{matrix} y & m & q \\ x & l & p \\ z & n & r \end{matrix} | (int e r c h a n g i n g R_{1} a n d R_{2})$

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