If matrix \( A=\left[\begin{array}{lll}a & b & c \\ b & c & a \\ c ...

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If matrix \( A=\left[\begin{array}{lll}a & b & c \\ b & c & a \\ c & a & b\end{array}\right] \), where \( a, b, c \) are real
\( \mathrm{P} \)
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positive numbers such that \( a b c=1 \& A . A^{\mathrm{T}}=\mathrm{I} \). Find the value of \( a^{3}+b^{3}+c^{3} \).
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