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By using properties of determinants. Sho...

By using properties of determinants. Show that:`|[1+a^2-b^2, 2a b,-2b],[2a b,1-a^2+b^2, 2a],[2b,-2a,1-a^2-b^2]|=(1+a^2+b^2)^3`

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To show that \[ \left| \begin{array}{ccc} 1 + a^2 - b^2 & 2ab & -2b \\ 2ab & 1 - a^2 + b^2 & 2a \\ 2b & -2a & 1 - a^2 - b^2 \end{array} \right| = (1 + a^2 + b^2)^3, ...
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