# Math Help - [SOLVED] Linear algebra matrix problem

1. ## [SOLVED] Linear algebra matrix problem

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.

All I know is
AC = CA
BC = CB

But I don't know what to do with that information to prove this.

2. Originally Posted by paulrb
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.

All I know is
AC = CA
BC = CB

But I don't know what to do with that information to prove this.
Since $AC = CA\;\;\Rightarrow\;\;ACB = CAB\;\;\Rightarrow\;\; ABC=CAB$.

3. Thanks, that's a lot easier than I thought. I guess I was thinking too hard.