Prove that the matrix $I_n - A$ is invertible Let $A$ be an $n \times n$ matrix with the property that $A^3 = O_n$, where $O_n$ denotes the $n \times n$ matrix which
has all the entries equal to $0$. Let $I_n$ be the $n \times n$ identity matrix. Prove that the matrix $I_n - A$
is invertible, and indicate how you would obtain its inverse.

I think that it should read $I_n -A$ instead of $I_n \rightarrow A$.
Observe that
$ I_n=I_n-A^3=(I_n-A)(A^2+A+I_n)$
