Let $\displaystyle A$ be an $\displaystyle n \times n$ matrix such that $\displaystyle A^k = 0_{n,n}$ (the$\displaystyle n \times n$ zero matrix)
for some natural integer $\displaystyle k$. Show that I$\displaystyle _{n} + A$ is invertible.
Let $\displaystyle A$ be an $\displaystyle n \times n$ matrix such that $\displaystyle A^k = 0_{n,n}$ (the$\displaystyle n \times n$ zero matrix)
for some natural integer $\displaystyle k$. Show that I$\displaystyle _{n} + A$ is invertible.