How can $a^T(b-xa) = 0 $ means $xa^{T}a = a^Tb$?

Question

I was watching gilbert strang lectures on the projection matrix, at 5.17 he wrote that:

$a^T(b-xa) = 0 $

That means:

$xa^{T}a = a^Tb$

how can we write this expression?

In my opinion isn't it should be: $ a^Txa = a^Tb $ ?

Actually I am not good at linear algebra, so I know the question may be silly.

Answer 1

Because $x\in \mathbb{R}$ and then $a^T.xa=xa^T.a=x\|a\|^2$

Answer 2

Because, If you heard carefully,(at 2:50) he says that $\textbf{p}$ is scalar multiple of $\textbf{a}$ for some $x \in \mathbb{R}$

$$\textbf{p} = x.\textbf{a} , x \in \mathbb{R} , \textbf{a}^T. (x\textbf{a}) = x( \textbf{a}^{T}.\textbf{a})$$