By using the properties of determinants show that \[ \begin{array}{l} \begin{vmatrix} 1+a^2-b^2&2ab&-2b \\ 2ab&1-a^2+b^2&2a \\ 2b&-2a&1-a^2-b^2 \end{vmatrix} = (1+a^2+b^2)^3 \end{array} \]

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