Question

If $\omega (\ne 1)$ is a cube root of unity of $A=\left[\begin{array}{ccc}1+2{\omega }^{100}+{\omega }^{200}& {\omega }^2& 1\\ 1& 1+2{\omega }^{100}+{\omega }^{200}& \omega \\ \omega & {\omega }^2& 2+{\omega }^{100}+2{\omega }^{200}\end{array}\right]$, then

• A. $A$ is singular
• B. $|A|\ne 0$
• C. $A$ is symmetric
• D. none of these

Answer 1

The correct option is A $A$ is singular

MODE OF A IS EQUAL TO ZERO , SO THE MATRIX IS SINGULAR.