Given a matrix $A = [a b c b c a c a b], w h e r e a, b, c$ are real positive numbers $a b c = 1 a n d A^{T} A = I,$ then find the value of $a^{3} + b^{3} + c^{3} ˙$

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Given a matrix

A = [a b c b c a c a b], w h e r e a, b, c

are real positive numbers

a b c = 1 a n d A^{T} A = I,

then find the value of

a^{3} + b^{3} + c^{3} ˙

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Question Text

Given a matrix

A = [a b c b c a c a b], w h e r e a, b, c

are real positive numbers

a b c = 1 a n d A^{T} A = I,

then find the value of

a^{3} + b^{3} + c^{3} ˙

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