Suppose a, b, c ∈ R and a b c=1, if A=[[ 3 a b c; b 3 c a; c a 3 b ]] is such that A^...

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Suppose a, b, c ∈ R and a b c=1, if A=[[ 3 a b c; b 3 c a; c a 3 b ]] is such that A^T A=4^1 / 3 I and |A|0, the value of a^3+b^3+c^3 is

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