Let a, b, c $ \in $ R be all non-zero and satisfy a3 + b3 + c3 = 2. If the matrix A = $$\left( {\matrix{ a & b & c \cr b & c & a \cr c & a & b \cr } } \right)$$ satisfies ATA = I, then a value of abc can be :

Question

Let a, b, c $ \in $ R be all non-zero and satisfy
a³ + b³ + c³ = 2. If the matrix

A = $$\left( {\matrix{ a & b & c \cr b & c & a \cr c & a & b \cr } } \right)$$

satisfies A^TA = I, then a value of abc can be :

${1 \over 3}$