Let $1, \omega$ and $\omega^2$ be the cube roots of unity. If $\mathrm{S}$ is the set of all non-singular matrices of the form $\left[\begin{array}{rrr}1 & a & b \ \omega & 1 & c \ \omega^2 & \omega & 1\end{array} ight]$ where $a, b, c \in\left\{\omega, \omega^2 ight\}$, then the number of…

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Let $1, \omega$ and $\omega^2$ be the cube roots of unity. If $\mathrm{S}$ is the set of all non-singular matrices of the form $\left[\begin{array}{rrr}1 & a & b \ \omega & 1 & c \ \omega^2 & \omega & 1\end{array}ight]$ where $a, b, c \in\left\{\omega, \omega^2ight\}$, then the number of elements in $\mathrm{S}$ is

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Let $1, \omega$ and $\omega^2$ be the cube roots of unity. If $\mathrm{S}$ is the set of all non-singular…

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