Solve Invertible Matrix Problem: Find Equivalent Conditions to "A is Invertible

[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

 

[Dick]

Name one. You aren't trying very hard.

 

[eyehategod]

i don't understand the question

 

[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?

 

[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.

 

[mkwok]

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