1. ## Matrices and inverses

Let A and B be n*n matrices and let their product AB be invertible.
Prove A and B are invertible

2. ## Re: Matrices and inverses

Originally Posted by I-Think
Let A and B be n*n matrices and let their product AB be invertible.
Prove A and B are invertible
Let C be the inverse of AB, then C(AB) = (AB)C = I.
Now use associativity in the above expression. do you see it?

3. ## Re: Matrices and inverses

Another way to see why it "should be" true is to consider the identity det(AB)=det(A)det(B). Isomorphism's answer is definitely more straightforward, though.