If Matrix $A^3 = 0$ then what will be $I+A+A^2$ Matrix $A$ is a square matrix such that $$A^3=0$$ then what would be value of $$I+A+A^2=?$$ such that $I$ is unit matrix of same order as $A$
I firstly supposed sum to be $X$ that is 
$X=I+A+A^2$ then 
$$AX=A+A^2+A^3$$
$$AX=A+A^2$$
and multiplying both sides with $A^{-1}$ we get 
$$K=I+A$$ but my answer was incorrect , what is correct solution to this problem?

$$(I+A+A^2)(I-A)=I-A^3=I$$
Hence $I+A+A^2=(I-A)^{-1}$.
