# Homework Help: Invertible matrix

1. Nov 4, 2007

### eyehategod

I have to write all possible equivalent conditions to "A is invertible," where A is an nxn matrix. can anyone help me out with this question

2. Nov 4, 2007

### Dick

Name one. You aren't trying very hard.

3. Nov 4, 2007

### eyehategod

i dont understand the question

4. Nov 4, 2007

### rock.freak667

well you know that A^-1 = 1/det|A| *adj(A)

so for this to exist...det|A| can't be zero...and think of row-echelon form when finding A^-1

in row-echelon form, to get A^-1. how many non-zero rows must it have?How many pivot positions must it have?

5. Nov 4, 2007

### Dick

Here's another one. A is invertible if there is a matrix B such that A*B=I. You are way behind. How about a statement in terms of the dimension of the kernel? How about expressing invertability in terms of the solutions to a system of linear equations? There's a lot of ways to express this concept.

6. Nov 4, 2007

### mkwok

A is also invertible when the determinant does not equal to 0