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![Prove that |[1 +a^2 -b^2, 2ab, -2b],[2ab, 1-a^2 +b^2, 2a],[2b, -2a, 1-a^2 -b^2]| = (1 + a^2 + b^2)^3](http://i.ytimg.com/vi/B7UwIYXEcX8/mqdefault.jpg "Prove that |[1 +a^2 -b^2, 2ab, -2b],[2ab, 1-a^2 +b^2, 2a],[2b, -2a, 1-a^2 -b^2]| = (1 + a^2 + b^2)^3")