1. Elem. Linear Alg.

Hi guys,

I took "baby" linear algebra over the summer and now I'm in calc III and we do a mini-linear algebra unit at the end of Calc III. Unfortunately, I don't have my old linear algebra book to use as a reference which is truly unfortunate. If someone could get help me get my wheels churning on a few problems I would really appreciate it!

If matrices A and B are invertible, show that $(AB)^{-1}=B^{-1}A^{-1}$

2. Just go by definition. If A is a square matrix and there exists another matrix B such that $AB = BA = I$, then B is the inverse of A.

So, all you have to show is that: $(AB)\left(B^{-1}A^{-1}\right) = \left(B^{-1}A^{-1}\right)(AB) = I$