I am a newbie in GA. I am going through the Doran’s book and I stumped onto the demonstration the outer product is associative in section 2.4

For a start it decomposes

a\wedge(b\wedge c)=\frac 1 2 (\,a(b\wedge c)+(b \wedge c)a\,)

However I dont understand the reason for the + symbol.

According to the formulaes in section 2.1:

p\wedge q=\frac 1 2 (pq-qp)

So calling a=p and b\wedge c=q

the abobe formula should be:

a\wedge(b\wedge c)=\frac 1 2 (\,a(b\wedge c)\textcolor{red}{-}(b \wedge c)a\,)

Problem is whith + the demonstration works, and whith the - does not.