Hi all, I got stuck on this question when it came to proving the identity.

I can't find anything that helps in my notes or textbook, except that I should write

$\displaystyle \displaystyle\sum_{r=1}^n (x_r-\mu)^T\Sigma^-^1(x_r-\mu) = \displaystyle\sum_{r=1}^n (x_r-\bar{x}+\bar{x}-\mu)^T\Sigma^-^1(x_r-\bar{x}+\bar{x}-\mu)$.