prove that $∣ ∣ a^{2} + 1 a b a c a b b^{2} + 1 b c a c b c c^{2} + 1 ∣ ∣ = 1 + a^{2} + b^{2} + c^{2} .$

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prove that

∣ ∣ a^{2} + 1 a b a c a b b^{2} + 1 b c a c b c c^{2} + 1 ∣ ∣ = 1 + a^{2} + b^{2} + c^{2} .

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Question Text

prove that

∣ ∣ a^{2} + 1 a b a c a b b^{2} + 1 b c a c b c c^{2} + 1 ∣ ∣ = 1 + a^{2} + b^{2} + c^{2} .

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