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Show that , A^(-1) = (1)/(3) [(-1,2,-2),...

Show that , `A^(-1) = (1)/(3) [(-1,2,-2),(-2,1,-2),(2,2,1)]` is a proper orthogonal matrix.

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STATEMENT -1 : A=(1)/(3){:[(1,-2,2),(-2,1,2),(-2,-2,-1)]:} is an orthogonal matrix and STATEMENT-2 : If A and B are otthogonal, then AB is also orthogonal.