# [SOLVED] Linear algebra matrix problem

• February 23rd 2009, 06:53 AM
paulrb
[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.
• February 23rd 2009, 06:57 AM
Jester
Quote:

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 $AC = CA\;\;\Rightarrow\;\;ACB = CAB\;\;\Rightarrow\;\; ABC=CAB$.
• February 23rd 2009, 07:03 AM
paulrb
Thanks, that's a lot easier than I thought. I guess I was thinking too hard.