# Homework Help: Linear algebra

1. Feb 25, 2010

1. The problem statement, all variables and given/known data

state if the statement if it's true or false (give a brief explanation if it's true or give a counter example if it's false)

2. Relevant equations
If A is an invertible nxn matrix, then A^m is not equals to O_m,n for all natural m

3. The attempt at a solution
what is O_m,n?

2. Feb 25, 2010

### CompuChip

I presume it would be the zero matrix (the unique m x n matrix all whose entries are 0).

3. Feb 25, 2010

### HallsofIvy

In other words, if A is an invertible matrix, is it possible to have $A^n= 0$ for some n? Start multiplying both sides of $A^n= 0$ by $A^{-n}$. "Repeat as needed".

4. Feb 25, 2010

### CompuChip

I would choose another approach, where the hint "consider the determinant" applies.