# Matrix finds the cube

Algebra Level 4

Let $$A = \left( \begin{matrix} a & b & c \\ b & c & a \\ c & a & b \end{matrix} \right)$$ be a matrix where $$a, b, c$$ are complex numbers. If $$abc = 1$$ and $$A^T A = I$$, what is the value of $$a^3 + b^3 + c^3$$?

Clarification: $$A^T$$ is the transpose of $$A$$. $$I$$ is the identity matrix of order $$3 \times 3$$.

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