Matrix - own
Posted: Tue Jun 12, 2012 6:06 am
Let $A$ be an $n\times n$ real matrix ($n\in\mathbb N$). Suppose that all entries in the first column of $A^n$ are zero, but not all entries in the first column of $A^{n-1}$ are zero. Prove that all entries of $A^n$ are zero.