# Commutative multiplication

1. Sep 12, 2009

### Butelle

1. The problem statement, all variables and given/known data

I am trying to prove an identity and in order to finish the proof i need to show that:
for z a p-dimensional vector and A a non-singular square (pXp) matrix - also note that T is transpose - :
zTA^(-1)z = zzTA^(-1), where -1 denotes the inverse

I have looked everywhere to find vector multiplication that commutes but so far can't find a rule...

2. Sep 12, 2009

### gabbagabbahey

That doesn't look right to me...$z^TA^{-1}z$ is a scalar (assuming $z$ is a column vector), while $zz^TA^{-1}$ is a $p\times p$ matrix.....what was the original problem?

3. Sep 13, 2009

### Butelle

Hey Gabby - thank you for pointing that out (i can't believe i didnt see that!).

I will try it again now - maybe I have done some stupid mistake.