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If $\begin{vmatrix}a&b&0\\0&a&b\\b&0&a\end{vmatrix}=0$, then |
a/b is one of the cube roots of unity a is one of the cube roots of unity b is one of the cube roots of unity a/b is one of the cube roots of -1 |
a/b is one of the cube roots of -1 |
We have, $\begin{vmatrix}a&b&0\\0&a&b\\b&0&a\end{vmatrix}=0$ $⇒a^3+b^3=0$ [On expanding the determinant on LHS] $⇒(a/b)^3=-1$ ⇒ a/b is one of the cube roots of -1 |
