Help with a simple matrix proof

[paulrb]

Edit: Sorry, I figured this out shortly after posting. It's a simple problem but I hadn't used matrix equations before.

Homework Statement

If A, B, and C are all square matrices of the same size, show that AB commutes with C if A and B both commute with C.

Homework Equations

Formula for matrix multiplication

The Attempt at a Solution

All I know is
AC = CA
BC = CB
A, B, and C are square matrices of the same size

I want to prove that (AB)(C) = (C)(AB).
But I am not sure how to do this, or even how to get started.

 

[Daettil]

Well Matrix multiplication is associative so you should be able to manipulate (AB)C to get C(AB) pretty easily.