Make the correct alternative in following question:

Let $\mathrm{P}(n): x^{n}-1$ is divisible by $(x-\lambda)$.

As, for $n=1$,

$\mathrm{P}(1)=x^{1}-1=x-1$

As, $\mathrm{P}(1)$ must be divisible by $(x-\lambda)$.

$\Rightarrow(x-1)$ must be divisible by $(x-\lambda)$.

So, $\lambda=1$

Hence, the correct alternative is option (a).