# $\bf{\mu}_i$ and $\bf{\mu}_j$ have the same dimension, can I derive…?

If the vectors $$\bf{\mu}_i$$ and $$\bf{\mu}_j$$ have the same dimension, can I derive that $$\mu_1^T\Sigma^{-1}\mu_1-\mu_2^T\Sigma^{-1}\mu_2=(\mu_1^T-\mu_2^T)\Sigma^{-1}(\mu_1-\mu_2)$$?

$$(\mu_1^T-\mu_2^T)\Sigma^{-1}(\mu_1-\mu_2) = \mu_1^T \Sigma^{-1}\mu_1 + \mu_2^T \Sigma^{-1}\mu_2 - \mu_2^T \Sigma^{-1}\mu_1 - \mu_1^T \Sigma^{-1}\mu_2.$$
Let $$\mu_1 = (1,2)^T$$, $$\mu_2=(1,3)^T$$, $$\Sigma=\begin{pmatrix} 1&0\\0&4\end{pmatrix}$$.
$$\mu_1^T\Sigma^{-1}\mu_1-\mu_2^T\Sigma^{-1}\mu_2=-\frac{5}{4}$$
$$(\mu_1^T-\mu_2^T)\Sigma^{-1}(\mu_1-\mu_2)=\frac{1}{4}$$