## Matrix - own

For college and university level advanced Mathematics
nayel
Posts: 268
Joined: Tue Dec 07, 2010 7:38 pm
Location: Dhaka, Bangladesh or Cambridge, UK

### Matrix - own

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.
"Everything should be made as simple as possible, but not simpler." - Albert Einstein