Question

P is a non singular matrix and $I+p+p^2+......+p^n=0$ then $p^{-1}$ is

• A. $p^n$
• B. $p^{n-1}$
• C. $-p^n$
• D. $-p^{n-1}$

Answer 1

The correct option is A $p^n$

$I+p+p^2+.....p^n=0.$ ------ $\left(1\right)$

Pre multiply by $p-1$

$p^{-1}+\underset{-p^n\left[from\right(1\left)\right]}{\underset{}{I+p+p^2+....p^{n-1}}}=0$

$p^{-1}-p^n=0$

$p^{-1}=p^n$

$A$ is correct.