By using properties of determinants. Show that: $∣ ∣ 1 + a^{2} - b^{2} 2 a b - 2 b 2 a b 1 - a^{2} + b^{2} 2 a 2 b - 2 a 1 - a^{2} - b^{2} ∣ ∣ = (1 + a^{2} + b^{2})^{3}$

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By using properties of determinants. Show that:

∣ ∣ 1 + a^{2} - b^{2} 2 a b - 2 b 2 a b 1 - a^{2} + b^{2} 2 a 2 b - 2 a 1 - a^{2} - b^{2} ∣ ∣ = (1 + a^{2} + b^{2})^{3}

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Question Text

By using properties of determinants. Show that:

∣ ∣ 1 + a^{2} - b^{2} 2 a b - 2 b 2 a b 1 - a^{2} + b^{2} 2 a 2 b - 2 a 1 - a^{2} - b^{2} ∣ ∣ = (1 + a^{2} + b^{2})^{3}

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