<s>[INST] Where can I read about this 'rule'? I was trying to solve an equation, I got nowhere, and the solution used a 'rule' that I have never seen before, $a^TX\,b = b^TX\,a$. 
What is this rule?
Where can I read about it?
Note: $a$ and $b$ are vectors and $X$ is a matrix.
 [/INST] a^t is for transpose, right?
$
        \begin{pmatrix}
        a_1 & a_2  \\
        \end{pmatrix}
$$
        \begin{pmatrix}
        x_{11} & x_{12}  \\
        x_{21} & x_{22} \\
        \end{pmatrix}
$$
        \begin{pmatrix}
        b_1 \\ b_2  \\
        \end{pmatrix}
$ = $a_1b_1x_{11} + a_2b_1x_{21} + a_1b_2x_{12} + a_2b_2x_{22} $
but
$
        \begin{pmatrix}
        b_1 & b_2  \\
        \end{pmatrix}
$$
        \begin{pmatrix}
        x_{11} & x_{12}  \\
        x_{21} & x_{22} \\
        \end{pmatrix}
$$
        \begin{pmatrix}
        a_1 \\ a_2  \\
        \end{pmatrix}
$ = $a_1b_1x_{11} + a_1b_2x_{21} + a_2b_1x_{12} + a_2b_2x_{22} $
So, if X is symmetrical, ($x_{12} = x_{21}$), then this rule is true just by doing multiplication. 
</s>