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Given a matrix A=[(a,b,c),(b,c,a),(c,a,b...

Given a matrix `A=[(a,b,c),(b,c,a),(c,a,b)]`, where a, b, c are real positive numbers. If `abc=1` and `A^(T)A=I`, then find the value of `a^(3)+b^(2)+c^(3)`.

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