Without expanding the determinant prove that a p - b q m c r n - r n c q m b p - a - 0

We have nbsp; a amp; p amp; ℓ b amp; nbsp;q amp; m c amp; r amp; n + C_1 ↔ C_3 r amp; n amp; c nbsp;q amp ...

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Properties of Determinants

Without expan...

Question

Without expanding the determinant prove that $∣ ∣ ∣ ∣ \begin{matrix} a & p & ℓ b & q & m c & r & n \end{matrix} ∣ ∣ ∣ ∣ + ∣ ∣ ∣ ∣ \begin{matrix} r & n & c q & m & b p & ℓ & a \end{matrix} ∣ ∣ ∣ ∣ = 0$

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