$x^T \Sigma^{-1} y = y^T \Sigma^{-1} x$?

Question

If $\Sigma^{-1}$ is a symmetric matrix (a covarince matrix, precisely), and $x, y$ are vectors of equal dimension, is it true that $x^T \Sigma^{-1} y = y^T \Sigma^{-1} x$?

While walking through the solution to the problem of Maximum Likelihood Estimation of Gaussian Distribution (details not necessary here), I encountered this property being used multiple times. Also, the following occurs in one of the steps:

$( x^{T} - y^{T}) \Sigma^{-1}$ = $\Sigma^{-1}( x - y) $

Can someone help me understand these results?

Thank you.

Edit: As mentioned by someone in the comments, the second result may not be correct, I am not sure why it is mentioned in the solution to the problem.

Answer 1

Since $\Sigma$ is symmetric, so is $\Sigma^{-1}$. Thus $$x^T\Sigma^{-1}y=\sum_{i,j}(\Sigma^{-1})_{ij}x_iy_j=\sum_{i,j}(\Sigma^{-1})_{ji}x_iy_j=y^T(\Sigma^{-1})x.$$