# Nxn Matrix AB=I?

1. Feb 19, 2014

### sheldonrocks97

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

Prove that every n x n matrix A for which there exists an n x n matrix B such that AB = I must be invertible. Hint: Use properties of determinants.

2. Relevant equations

None that I am aware of.

3. The attempt at a solution

I tried finding the inverse of the matrix and multiplying by an elementary matrix. I also tried finding the determinants of a simple matrix and using it's properties but nothing is working :(
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Feb 19, 2014

### pasmith

You are supposed to use the fact that $\det (AB) = (\det A) (\det B)$.