Let $\omega$ be a complex cube root of unity with $\omega
eq 1$ and $P=\left[p_{i j} ight]$ be a $2 imes 2$ matrix with $p_{i j}=\omega^{i+j}$. For $P^2
eq 0$ if $P^k=P$, then $k$ is equal to

Question

Let $\omega$ be a complex cube root of unity with $\omega 
eq 1$ and $P=\left[p_{i j}ight]$ be a $2 	imes 2$ matrix with $p_{i j}=\omega^{i+j}$. For $P^2 
eq 0$ if $P^k=P$, then $k$ is equal to

Aicharya · Accepted Answer

No solution. Refer to answer key.

Let $\omega$ be a complex cube root of unity with $\omega \neq 1$ and $P=\left[p_{i j}\right]$ be a $2…

Solution