Why Aren't AXB and BXA Equal in Matrix Multiplication?

[jcsolis]

Homework Statement

Show that AXB is not equal to BXA

No variables given..just this equation

Homework Equations

The Attempt at a Solution

I don´t know how to start...the only thing I know so far is that AXB is equal to -BXA

 

[Hurkyl]

Have you tried any examples at all? After all, if you know that AxB = -BxA, shouldn't it be very easy to find a counterexample?

 

[jcsolis]

let me try

 

[Hurkyl]

A little comment on semantics... when a question asks you to prove an identity is invalid; e.g. to show that AxB is not BxA, that means you just need to find one counterexample. In particular, the problem is not asking you to prove AxB and BxA are unequal for every possible A and B.

 

[jcsolis]

Thanks for the help...I didn´t understand why it´s not equal and now I get it