Originally Posted by

**ematb** In a proof I am studying a step uses a propriety of matrices I do not know, doing some tries it seems true but I can't find a way to prove it.

I'll use some almost-LaTeX

v \in R^{n \times 1}

u \in R^{1 \times n}

the propriety is:

(vu)^2 = (uv)(vu)

Where, of course, (uv) is a real number.

Probably I am just missing the obvious, but matrices multiplication isn't usually commutative. Those matrices are peculiar since made from products of vectors, but I can't see why it works.

Can you tell me how to prove it? (or prove it is wrong of course)