jee-advanced 2011 Q43

jee-advanced · India · paper2 Matrices Determinant and Rank Computation

Let $\omega \neq 1$ be a cube root of unity and $S$ be the set of all non-singular matrices of the form $$\left[ \begin{array} { c c c } 1 & a & b \\ \omega & 1 & c \\ \omega ^ { 2 } & \omega & 1 \end{array} \right]$$ where each of $a , b$, and $c$ is either $\omega$ or $\omega ^ { 2 }$. Then the number of distinct matrices in the set $S$ is
(A) 2
(B) 6
(C) 4
(D) 8

Let $\omega \neq 1$ be a cube root of unity and $S$ be the set of all non-singular matrices of the form
$$\left[ \begin{array} { c c c } 
1 & a & b \\
\omega & 1 & c \\
\omega ^ { 2 } & \omega & 1
\end{array} \right]$$
where each of $a , b$, and $c$ is either $\omega$ or $\omega ^ { 2 }$. Then the number of distinct matrices in the set $S$ is\\
(A) 2\\
(B) 6\\
(C) 4\\
(D) 8

Paper Questions

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