Solved: Proving matrices are commutative

[Ricemarine]

***Solved*** I get it now... Thanks LordMorpheus!

So one of the things I'm trying to understand right now is matrix multiplication...

So the problem is if AB is commutive (or AB = BA), then prove A^2 B^2 = (AB^2)

So what I am trying so far is using the associative law of multiplication which is
A(BC) = (AB)C

Starting off.

AB = BA

Multiplying both sides by A gives me

(AA)B = (BA)A

then multiplying both sides by B

B[(AA)B] = B[(BA)A)]

which becomes

AA * BB = BA * BA

= A^2B^2 = (AB)^2... <-- due to AB = BA.

Works as a proof? Or is it too short?

 

[LordMorpheus]

matrix multiplication isn't communitive.

But it can be in specific cases.

AB = BA show (AB)^2 = A^2B^2

(AB)^2 = ABAB

if AB = BA

ABAB = AABB

so (AB)^2=A^2B^2

 

[Ricemarine]

Originally posted by: LordMorpheus
matrix multiplication isn't communitive.

But it can be in specific cases.

AB = BA show (AB)^2 = A^2B^2

(AB)^2 = ABAB

if AB = BA

ABAB = AABB

so (AB)^2=A^2B^2

So I was supposed to use the fact AB = BA and resubstitute them into showing AB^2 = A^2B^2?

Edit: I actually don't see how you used if AB = BA to get from AB^2 = ABAB to ABAB = AABB... Did you switch the second side?...

Edit #2: ohh... you switched BA to AB... I get it...... I think... Let me try and understand this a bit more before I declare this solved.

 

[eLiu]

Doh, what a misleading thread title

I came in here all ready to do this.