# Matrices problem

kumarrukhaiyar
1. A square matrix A is called nilpotent if a^k = 0 for some k > 0. Prove that if A is nilpotent, then I + A is invertible.

2. Show that the equation AB - BA = I has no solutions in n x n matrices with real entries.

Homework Helper
Regarding 2, try to use the matrix trace function.